The power expended is 500 W
Explanation:
First of all, we start by calculating the work done by the man in order to ascend: this is equal to the gravitational potential energy gained by the man, which is
[tex]W=mg\Delta h[/tex]
where
m = 50 kg is the mass of the man
[tex]g=10 m/s^2[/tex] is the acceleration of gravity
[tex]\Delta h = 5 m[/tex] is the change in height
Substituting,
[tex]W=(50)(10)(5)=2500 J[/tex]
Now we can calculate the power expended, which is given by
[tex]P=\frac{W}{t}[/tex]
where
W = 2500 J is the work done
t = 5 s is the time elapsed
Substituting, we find
[tex]P=\frac{2500}{5}=500 W[/tex]
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James threw a ball vertically upward with a velocity of 41.67ms-1 and after 2 second David threw a ball vertically upward with a velocity of 55.56ms-1.When the balls will be at the same height?
Answer:
When have passed 3.9[s], since James threw the ball.
Explanation:
First, we analyze the ball thrown by James and we will find the final height and velocity by the time two seconds have passed.
We'll use the kinematics equations to find these two unknowns.
[tex]y=y_{0} +v_{0} *t+\frac{1}{2} *g*t^{2} \\where:\\y= elevation [m]\\y_{0}=initial height [m]\\v_{0}= initial velocity [m/s] =41.67[m/s]\\t = time passed [s]\\g= gravity [m/s^2]=9.81[m/s^2]\\Now replacing:\\y=0+41.67 *(2)-\frac{1}{2} *(9.81)*(2)^{2} \\\\y=63.72[m]\\[/tex]
Note: The sign for the gravity is minus because it is acting against the movement.
Now we can find the velocity after 2 seconds.
[tex]v_{f} =v_{o} +g*t\\replacing:\\v_{f} =41.67-(9.81)*(2)\\\\v_{f}=22.05[m/s][/tex]
Note: The sign for the gravity is minus because it is acting against the movement.
Now we can take these values calculated as initial values, taking into account that two seconds have already passed. In this way, we can find the time, through the equations of kinematics.
[tex]y=y_{o} +v_{o} *t-\frac{1}{2} *g*t^{2} \\y=63.72 +22.05 *t-\frac{1}{2} *(9.81)*t^{2} \\\\y=63.72 +22.05 *t-4.905*t^{2} \\[/tex]
As we can see the equation is based on Time (t).
Now we can establish with the conditions of the ball launched by David a new equation for y (elevation) in function of t, then we match these equations and find time t
[tex]y=y_{o} +v_{o} *t+\frac{1}{2} *g*t^{2} \\where:\\v_{o} =55.56[m/s] = initial velocity\\y_{o} =0[m]\\now replacing\\63.72 +22.05 *t-(4.905)*t^{2} =0 +55.56 *t-(4.905)*t^{2} \\63.72 +22.05 *t =0 +55.56 *t\\63.72 = 33.51*t\\t=1.9[s][/tex]
Then the time when both balls are going to be the same height will be when 2 [s] plus 1.9 [s] have passed after David throws the ball.
Time = 2 + 1.9 = 3.9[s]
An object with a mass of 20 kg has a net force of 80 N acting on it. What is the acceleration of the object?
Answer:
4 m/s²
Explanation:
The formula used here:
F = ma
F is force (80 N)
m is mass (20 kg)
a is acceleration
Since we need to calculate acceleration we will arrange the formula:
a = F ÷ m
Now substitute the values and solve
a = 80 ÷ 20
a = 4
The proper unit for this acceleration is m/s²
So the object accelerates at 4 m/s²
Answer:
4 m/s^2
Explanation:
F = ma
80N = (20kg)a
80N/(20kg) = (20kg)a/(20kg)
4 m/s^2 = a
Help Meeeeee
Two kids are roller skating. Amy, with a mass of 55 kg, is traveling forward at 3 m/s. Jenny, who has a mass of 40 kg, is traveling in the opposite direction at 5 m/s. They crash into each other and hold onto each other so that they move as one mass. How fast are they traveling?
Answer:
0.4 m/s
Explanation:
From the law of conservation of momentum, the sum of initial momentum equals the sum of final momentum
Momentum, p=mv where m is the mass and v is the velocity
[tex]m_1v_1+m_2v_2=(m_1+m_2)v_c[/tex] where [tex]v_c[/tex] is the common velocity, [tex]v_1[/tex] and [tex]v_2[/tex] are velocities of Amy and Jenny respectively, [tex]m_1[/tex] and [tex]m_2[/tex] are masses of Amy and Jenny respectively.
Taking forward direction as positive, opposite direction is negative hence [tex]v_1[/tex] is 3 m/s while [tex]v_2=-5 m/s[/tex]
[tex]55 kg\times 3 m/s +(40 kg\times -5 m/s)=(55 kg+40 kg)v_c[/tex]
[tex]95 kg v_c=-35 kg.m/s[/tex]
[tex]v_c=\frac {-35}{95}=-0.368421053 m/s\approx -0.4 m/s[/tex]
Therefore, they travel at 0.4 m/s in the direction of Jenny's movement
The infection where the air sacs in the lungs fill up with fluids is called:
A.
Pneumonia
B.
COPD
C.
Sleep apnea
D.
None of the above
Answer:
A
Explanation:
Pneumonia
Analyze the following terms and phrases about solar activity. Select the two that represent correct matches between cause and effect.(1 point)
a) solar activity -- sudden eruptions of large bubbles of plasma and magnetic energy
b) coronal mass ejection -- relatively cool spot on surface of the sun
c) sun's magnetic field -- uneven churning of the sun's gravitational field
d) solar flare -- sudden release of magnetic energy
e) sunspot -- magnetic field of the sun emerges as a loop
Answer:
a) solar activity -- sudden eruptions of large bubbles of plasma and magnetic energy
and
d) solar flare -- sudden release of magnetic energy
Explanation:
We can start by eliminating the options that are definitely wrong.
A coronal mass ejection is not a relatively cool spot on surface of the sun, in fact such a spot is a sunspot, while a coronal mass ejection occurs when the magnetic field of the sun emerges as a loop. Thus, both options B and E are incorrect, leaving only A, C, and D. Option C makes no sense, as the sun's gravitational field does not 'churn'. Thus, only options A and D are left. A closer look at A and D reveals they are correct; solar flares are in fact sudden releases of magnetic energy, as seen in this quote from UC Berkeley's website; "Solar flares are caused by sudden changes of strong magnetic fields in the Sun's corona.". And solar activity is a blanket term for the effects of eruptions of plasma and magnetic energy from the sun.
explain why when someone uses his thumb to push a pin into a block of wood the pressure on the wood is greater than the pressure on this thumb
When someone uses his thumb to push a pin into a block of wood the pressure on the wood is greater than the pressure on this thumb because the area of the pin on the thumb side is larger than the area of the pin on the wood side
What is pressure?The total applied force per unit of area is known as the pressure.
The pressure depends both on externally applied force as well the area on which it is applied.
The mathematical expression for the pressure
Pressure = Force /Area
the pressure is expressed by the unit pascal or N /m²
Since, the area of the pin on the thumb side is larger than the area of the pin on the wood side, when someone uses his thumb to push a pin into a block of wood, the pressure on the wood is greater than the pressure on this thumb.
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Two persons A and B do same amount of work. The person A does that work in t1sec and the person b in t2sec. Find the ratio of power delivered by them.
The ratio between power of A and power of B is 2
Explanation:
In physics, power is defined as the ratio between the work done and the time taken to do the work:
[tex]P=\frac{W}{t}[/tex]
where
P is the work done
t is the time taken
In this problem, we have:
Person A and person B do the same amount of work --> let's call this work W
Person A does this work in a time of [tex]t_A = 1 s[/tex], so the power delivered by A is
[tex]P_A = \frac{W}{1}=W[/tex]
Person B does this work in a time of [tex]t_B = 2 s[/tex], so the power delivered by B is
[tex]P_B = \frac{W}{2}[/tex]
So, the ratio of the powers delivered by the two persons is
[tex]\frac{P_A}{P_B}=\frac{W}{W/2}=2[/tex]
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please help me i don't get it
Answer:
39)
a) distance traveled = 1 mile
b) displacement = 0 mile
40) - 4 (m/s)
41-) distance traveled = 5 [m]
displacement = 3.6 [m]
Explanation:
The distance differs from the displacement, the distance traveled is equal to the sum of all displacements made by the particle or object.
Displacement is the difference between the initial point and the final point where the object or particle was stopped.
Then we can use the equation given:
[tex]a=\frac{(v_{f} - v_{i} )}{t} \\where:\\v_{f}=16[m/s]\\v_{i}=2[m/s]\\t=3.5[s]\\a=\frac{(2-16)}{3.5}\\ a=-4[m/s][/tex]
The minus sign means the particle is slowing down.
For the 41) we can see the attached image.
In the graph we can see that the particle moves north 3 miles, so that the first distance is 3 miles, then moves 2 miles east being the second distance of 2 miles. Thus the sum of the distances is 3 + 2 = 5 miles.
Displacement is the difference between the endpoint and the initial point since the form of displacement is a straight line, we can use the formula of the straight line or the theorem of Pythagoras.
[tex]d=\sqrt{(2-0)^{2}+(3-0)^{2} }\\d=3.6 [mi][/tex]
A 10kg rocket is traveling at 80 m/s when the booster engine applies a constant forward force of 60 N for 3.0 seconds. What impulse
does the booster engine supply? What is the resulting velocity of the rocket?
Answer:
Impulse = 90
Resulting Velocity = 89
Explanation:
Use F * change in time = m * change in velocity.
For the first part of the question, the left side of the equation is the impulse. Plug it in.
60 * (3.0 - 0) = 90.
For the second half. we use all parts of the equation. I'm gonna use vf for the final velocity.
60 * (3.0 - 0) = 10 * (vf - 80). Simplify.
90 = 10vf - 800. Simplify again.
890 = 10vf. Divide to simplify and get the answer.
The resulting velocity is 89.
The impulse supplied by the booster engine is 180 Ns and the resulting velocity of the 10kg rocket is 98 m/s.
The question involves calculating the impulse delivered by the booster engine of a rocket and its resulting velocity. The impulse is obtained through the relationship Impulse = Force × Time. By applying a constant forward force of 60 N for 3.0 seconds, the impulse can be calculated as:
Impulse = 60 N × 3.0 s = 180 Ns (Newton-seconds)
To find the resulting velocity of the rocket, we use the impulse-momentum theorem which states that the impulse applied to an object is equal to the change in momentum of the object. Since the rocket's mass is constant, the change in momentum can also be expressed as the mass of the rocket times the change in velocity (Impulse = Change in momentum = Mass × Change in velocity). Therefore:
Change in velocity = Impulse / Mass
Change in velocity = 180 Ns / 10 kg = 18 m/s
The initial velocity of the rocket is 80 m/s, so the final velocity of the rocket after the impulse will be:
Final velocity = Initial velocity + Change in velocity = 80 m/s + 18 m/s = 98 m/s
a 75 kilogram boy initally at rest skis down the slope as shown assuming no frictional loss what will be his kinetic energy at the bottom of the slope
Answer:
The kinetic energy at bottom, K.E = 73500 J
Explanation:
Given data,
The mass of the boy, m = 75 kg
Let the height of the hill be, h = 100 m
The P.E is maximum at the top of the hill. Since the boy is at rest at the top of the hill, his K.E is zero.
When he reaches the bottom, his K.E is maximum and P.E is zero.
According to the law of conservation of energy, K.E at the bottom is equal to the P.E at top.
P.E = mgh
= 75 x 9.8 x 100
= 73500 J
Hence, the kinetic energy at bottom, K.E = 73500 J
A rubbit gets down from a rump which its /\x=0.85m in 0.5s, The rubbit's mass is 2kg, what is the net Force?
Answer: 13.6 N
Explanation:
The equation of motion for the rabbit is:
[tex]\Delta x=V_{ox}t+\frac{1}{2}a_{x}t^{2}[/tex] (1)
Where:
[tex]\Delta x=0.85 m[/tex] is the distance traveled by the rabbit
[tex]V_{ox}=0 m/s[/tex] is the rabbit's initial velocity, assuming it started from rest
[tex]t=0.5 s[/tex] is the time
[tex]a_{x}[/tex] is the acceleration
Isolating [tex]a_{x}[/tex]:
[tex]a_{x}=\frac{2 \Delta x}{t^{2}}[/tex] (2)
[tex]a_{x}=\frac{2 (0.85 m)}{(0.5)^{2}}[/tex] (3)
[tex]a_{x}=6.8 m/s^{2}[/tex] (4)
On the other hand, the force [tex]F_{x}[/tex] is given by:
[tex]F_{x}=m.a_{x}[/tex] (5)
Where [tex]m=2 kg[/tex] is the mass of the rabbit
Substituting (4) in (5):
[tex]F_{x}=(2 kg)(6.8 m/s^{2})[/tex] (6)
Finally:
[tex]F_{x}=13.6 N[/tex]
A snowboard has a mass of 1.53 kg. What is the static frictional force on the snowboard if the
waxed snowboard was lying horizontally on a wet & snowy surface (u s = 0.2)?
Answer:
Static friction, F=2.9988 N
Explanation:
Static Friction: It is the friction between two or more solid body that are not moving relative to each other.
When an external force is applied to a body that is in contact with another body, static friction opposes the applied force upto a certain limit, keeping the body at rest. When the applied force exceeds the certain limit the body begins to move. At that moment applied force is equal to limiting value of static friction F.
It varies linearly with normal force(N)
F∝N
F=μN (where μ is constant of proportionality and known as coefficient of static friction)
Now,
Mass, m=1.53 kg
Coefficient of static friction, μ=0.2
Normal force, N=m×g
=[tex]1.53\times9.8[/tex] (g=9.8 m/s²)
=14.994 N
Static friction, F= μN
=[tex]0.2\times14.994[/tex]
= 2.9988 N
what is the displacement for a person that walks 3.0km north and 8.0 km south
Answer:
5 km
Explanation:
x = |3 - 8| = 5 km
What is the kinetic energy of a 50-kg child running to catch the school bus at
2 m/s?
O A. J
O B. 25 J
O C. 100J
O D. 200
Answer:
Option C
100 J
Explanation:
Kinetic energy, KE is given by
[tex]KE=0.5mv^{2}[/tex] where m is the mass and v is the velocity
Substituting 50 Kg for mass, m and 2 m/s for velocity v then we obtain
[tex]KE=0.5*50*2^{2}=100 J[/tex]
Therefore, the child's kinetic energy is equivalent to 100 J
Answer:100J
Explanation:
this is the process of organisms adapting to he environment overtime
Natural selection is the process of organisms adapting to their environments over time.
Explanation:
Natural selection refers the process to various survival and multiplication of organisms due to environmental properties. For example peacock, pepper moth, etc. These lead to evolutionary changes in which individual with specific traits has higher survival or reproduction than individuals in other populations and passes on these hereditary genetic traits to their offspring.
A process in which organisms are well suited to the surroundings than others generate more offspring. Due to this process, the percentage of organisms that adapt to the environment is increasing with each generation.
Which statements describe both male and female reproductive systems? Check all that apply. A:The reproductive system produces hormones. B:The reproductive system transports reproductive cells. C:The reproductive system produces reproductive cells. D:The reproductive system includes the urinary bladder. E:The reproductive system develops and nourishes a developing baby.
Answer: A:The reproductive system produces hormones.
B:The reproductive system transports reproductive cells.
C:The reproductive system produces reproductive cells.
Explanation:
A:The reproductive system produces hormones. : The reproductive organs ovaries in females and testes in males produces hormones. The ovaries produce estrogen and progesterone and testes produce testosterone.
B:The reproductive system transports reproductive cells. : The ovaries in females transfers an egg into the fallopian tube and testes in males secrete sperms at the time of copulation the fertilization of egg and sperm leads to the development of zygote the precursor of new life.
C:The reproductive system produces reproductive cells.: The ovaries undergo oogenesis and in testes spermatogenesis takes place to develop egg and sperms respectively.
The statements describing the reproductive system are production of hormones and gamete along with the transport. Thus, statements A, B and C are correct.
The reproductive system has been the organ system in the human body that has been function for the reproduction of the organism.
Functions of Reproductive systemThe reproductive system in males has been comprised of testes that produces the male hormones' testosterone. The female reproductive system has been comprised of the ovaries that has been producing estrogen and progesterone.
The male and female reproductive system are responsible for producing male and female gamete and transport them for reproduction.
Thus, the statements describing the reproductive system are production of hormones and gamete along with the transport. Thus, statements A, B and C are correct.
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how do you relate between magnetic field from current carrying wires with the force felt by a current carrying wire?
Answer:
"The magnetic field exert the force on current carrying wire in the direction of the individual charge particles moving."
Explanation:
The magnetic field that exert force in the current carrying wire in the same direction in which the charge particles moving came from the Right hand rule. The force are very higher that are sufficient to move the wire, hence, current particles have large number or moving particles in it. The wires through which current is flowing attract each other even in same direction because of the right hand rule only and also the formation of the magnetic field around the wire. The lines of force are the magnetic field.
The moon is not seen at all on the new moon.why???
The moon is not seen at all on the new moon because:
The moon itself doesn't make a light, it reflects sunlight. At the point when the moon lies between the Earth and the Sun, it is just the posterior of the moon that is light by the Sun. In this circumstance, the side of the moon confronting the Earth can't mirror any light whatsoever and seems dull.
The distinction between another moon and a sunlight based over-shadowing is during a sun oriented obscuration, the moon is actually in the position to completely obstruct the sun during the day.
Which of the following is the dot product of u = 4i + 6j – 5k and v=-10i – 8j + 10k?
Answer:
[tex]\vec u\ . \ \vec v=-138[/tex]
Explanation:
Dot Product of Vectors
The dot product of two vectors is also known as scalar product. Given the vectors
[tex]\vec u=4\hat i+6\hat j-5\hat k[/tex]
[tex]\vec v=-10\hat i-8\hat j+10\hat k[/tex]
The dot product is the sum of the products of each component separately
[tex]\vec u\ . \ \vec v=(4)(-10)+(6)(-8)+(-5)(10)[/tex]
[tex]\vec u\ . \ \vec v=-40-48-50=-138[/tex]
A wave with a period of three seconds travels at a speed of 12 m/s what is the wavelength of the wave
Answer:
λ = 0.28m
Explanation:
Equation used is v = λf, where v is velocity, λ is wavelength, and f is frequency
We need to find wavelength so rearrange the equation in term of wavelength.
v = λf
λ = f/v
We know that period is the inverse of frequency (f = 1/T), so lets substitute that into our equation
λ = f/v
λ = (1/T)/v
Plug in your the given values given in the question.
We're given v=12m/s and T=3sec
λ = (1/T)/v
λ = (1/3)/12
λ = 1/36 = 0.2777777 = 0.28m
Final answer:
The wavelength of a wave with a 3-second period traveling at 12 m/s is 36 meters.
Explanation:
To find the wavelength of a wave, you can use the formula:
wavelength = wave speed x period. In this case, the period of the wave (T) is 3 seconds and the wave speed (v) is 12 m/s.
wavelength = 12 m/s x 3 s = 36 meters.
Therefore, the wavelength of the wave is 36 meters.
What are the top three osha cited ladder violations
Answer: not having a portable ladder extend 3 feet above the landing
improper use of the top of step ladders
lack of work or training
Explanation: career safe online
The top three OSHA cited ladder violations are improper maintenance, improper use, and missing fall protection systems, endangering worker safety.
These violations are common because they relate to fundamental ladder safety. Maintaining a ladder's condition is crucial to ensure it's safe for use. Inadequate ladder use includes actions that increase the risk of falls, such as reaching too far or using a ladder not designed for the task.
Missing fall protection is a serious violation, especially when working at heights where a fall could lead to severe injuries or fatalities. Employers must ensure proper ladder training, maintenance, and use, and provide the necessary safety equipment to protect workers from fall hazards. Violations in these areas can result in OSHA citations and penalties.
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The force of attraction between the opposite charges of the ions in an ionic compound
The force of attraction between the opposite charges of the ions in an ionic compound is an ionic bond.
Explanation:
The transfer process of valence electron between atoms referred as ionic bond. This is a kind of chemical bonds which can create two oppositely charged ions. In the presence of ionic bonds, the metal loses electrons and becomes a positive charge cation, while non-metal accepts these electrons and becomes a negative charge anion.
Here, more than 1 electron can be emitted or received to meet the octet principle and the net charge of the compound should be zero. For example: Table salt. In this compound, sodium loses the electron to become [tex]N a^{+}[/tex], while the chlorine loses the electron to become [tex]c l^{-}[/tex].
The force of attraction between opposite charges of ions in an ionic compound is caused by electrostatic forces, forming what is known as an ionic bond. This creates stability in the compound and the strength of this attraction is measured by the lattice energy. While ionic compounds are generally poor electrical conductors in their solid state, they can become excellent conductors when dissolved or melted.
Explanation:The force of attraction between the opposite charges of the ions in an ionic compound, often referred to as an ionic bond, is a result of electrostatic forces. For instance, in sodium chloride or table salt, positively charged sodium ions bond with negatively charged chloride ions, forming a crystalline molecule with exception of any net charge. That's because of the attraction between the oppositely charged ions which keeps them in close proximity.
An ionic compound is stable due to this electrostatic attraction between its positive and negative ions. An important concept in this context is lattice energy: it's the energy required to separate a mole of a solid ionic compound into its gaseous ions, and is essentially a measure of the strength of the ionic bonds in the compound.
Ionic compounds, or salts, tend to be rigid and brittle, having high melting and boiling points - all indications of the strength of ionic bonds. They are poor conductors of electricity in solid state as the strength of these bonds prevents ions from moving freely, however, once dissolved or melted, ionic compounds turn into excellent conductors because the ions can now move freely.
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Which of the following describes the measure of current
Answer:
b. The rate at which charge flows
Explanation:
First we must complete the question:
Which of the following describes the measure of current:
a. The quality of the charge flow
b.The rate at which charge flows
c. The ability for something to have a charge flow
d.The potential for a charge to flow
The answer is b) The rate at which charge flows
The electric current is the electric charge flow that passes through a conductive material for a certain period of time. It is expressed in C / s, culombios per second in the international system of units, and the unit is known as Ampere (a)
The charge can be defined by culombio [C]
Different color ca
ferent color candy canes are tested to see
one type dissolves faster. What is the
independent variable?
Answer: The color of candy cane
Explanation:
An independent variable is the Variable that the scientist changed in order to change the dependent variable. The scientist changes the color of the candy cane to test the rate at which they dissolve.
Final answer:
The independent variable in this experiment is the color of the candy canes, while the dependent variable is the rate of dissolution. The student is testing different colors to see if they affect the dissolution rate.
Explanation:
The independent variable in this experiment is the different color of candy canes. The dependent variable is the rate at which each type of candy cane dissolves. By testing different colored candy canes, the student is investigating if there is a difference in the dissolution rate based on color.
Hi please help me with this question. ..
A man throws a stone upwards with a 'u' velocity and after spending ' t' seconds watching the motion of the stone he once again projects another stone upwards hoping that that these 2 stones should meet eachother. If his assumption is correct and these two stones collide with eachother, show that the 2 stones should meet each other 't/2 + u/g 'seconds later from the time of the first projection.
Explanation:
For projectile motion, use constant acceleration equation:
Δx = v₀ t + ½ at²
where Δx is the displacement,
v₀ is the initial velocity,
a is the acceleration,
and t is time.
Both objects are projected upward with velocity u. The second object is thrown after a time t₀.
For the first object:
Δx = u t + ½ (-g) t²
Δx = u t − ½g t²
For the second object:
Δx = u (t−t₀) + ½ (-g) (t−t₀)²
Δx = u (t−t₀) − ½g (t−t₀)²
Assuming the objects meet, the displacements will be equal:
u t − ½g t² = u (t−t₀) − ½g (t−t₀)²
u t − ½g t² = u (t−t₀) − ½g (t² − 2tt₀ + t₀²)
u t − ½g t² = u t − u t₀ − ½g t² + g tt₀ − ½g t₀²
0 = -u t₀ + g tt₀ − ½g t₀²
0 = -u + g t − ½g t₀
g t = u + ½g t₀
t = u/g + t₀/2
a 40.0 kilogram child exerts a 100 newton force on a 50.0 kilogram object the magnitude of the force that the object exerts on the child is?
A) 0.0N
B) 80.0N
C) 100N
D) 125N
Answer:
The answer is choice C.
Explanation:
According to Newtons third law of motion, the force that object exerts on the child is equal and opposite to the force that the child exerts on the object:
[tex]F_{child}=-F_{object}[/tex]
Thus if the child exerts a force of 100 newtons on the object, the object must also exert a force of 100 newtons on the child but in the opposite direction.
The magnitude of the force the object exerts on the child is 100 N.
The given parameters;
mass of the child, m = 40 kgforce exerted by the child, F = 100 Nmass of the object = 50 kgAccording to Newton's third law of motion, for every action there is an equal and opposite reaction.
The magnitude of the force the child exerted on the object is equal to the force the object exerted on the child.The direction of these forces are opposite.Thus, the magnitude of the force the object exerts on the child is 100 N.
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The position of an object along the x-axis is described by the formula x = 3t 2 − 2t. Which of the following are the correct formulas for the velocity and acceleration of the object?
Answer:
the formulas of velocity and acceleration can be given as:
Velocity : [tex]x'=6t-2[/tex]
Acceleration :[tex]x"=6[/tex]
Explanation:
Given:
The position function or formula for an object along x-axis is given by:
[tex]x=3t^2-2t[/tex]
To find the velocity and acceleration formulas.
Solution.
Velocity of an object is defined as rate of change of position of an object.
The rate of change can be found out by taking derivative of the position function of the object.
Thus the velocity formula can be written as:
[tex]x'=\frac{d}{dt}3t^2-\frac{d}{dt}2t[/tex]
[tex]x'=6t-2[/tex] [ As [tex]\frac{d}{da}a^n= na^{(n-1)}[/tex] and [tex]\frac{d}{da}na=n[/tex] ]
So, the velocity can be represented as [tex]x'=6t-2[/tex]
Acceleration of an object is defined as rate of change of velocity. In order to find rate of change of velocity, we will take derivative of the velocity function.
Thus the acceleration formula can be given as :
[tex]x''=\frac{d}{dt}6t-\frac{d}{dt}2[/tex]
[tex]x''=6[/tex] [ As [tex]\frac{d}{da}na=n[/tex] and [tex]\frac{d}{da}n=0[/tex] ]
So, the acceleration can be represented as [tex]x''=6[/tex]
The correct answer for the velocity and acceleration of the object described by the position formula x = 3t² - 2t are v = 6t-2 and a = 6. The correct option is d.
The correct formulas for the velocity and acceleration of the object described by the position formula x = 3t² - 2t are: v=6t-2 ; a=6
To find the velocity, we take the first derivative of the position equation with respect to time. The velocity is the derivative of position, so we differentiate x = 3t² - 2t to get v = 6t - 2. To find the acceleration, we take the second derivative of the position equation with respect to time. The acceleration is the derivative of velocity, so we differentiate v = 6t - 2 to get a = 6.
Complete Question:
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The position of an object along the x-axis is described by the formula x = 3t² - 2t. Which of the following are the correct formulas for the velocity and acceleration of the object?
a. [tex]$v=2 t^3-t, a=2 t-3$[/tex]
b. [tex]$v=6 t^2-4, a=12 t$[/tex]
c. [tex]$v=(1 / 2) t^3-2 t, a=(5 / 2) t^4-(2 / 3) t^2$[/tex]
d. v=6t-2, a=6
determine the proper unit for momentum using dimensionsal analysis
The unit for momentum is [tex]kg ms^{-1}[/tex]
Explanation:
The momentum of an object is defined as the product between the mass of the object and its velocity:
[tex]p=mv[/tex]
where
m is the mass of the object
v is its velocity
Let's determine the units for the momentum starting from the mass and the velocity:
The mass has units of kilograms, [tex]kg[/tex]The velocity has units of metres per second, [tex]ms^{-1}[/tex]Therefore, the unit for momentum is
[tex][p] = [m][v] = (kg)(ms^{-1}) = kg ms^{-1}[/tex]
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Final answer:
The proper unit for momentum, determined using dimensional analysis, is kilogram meters per second (kg·m/s), which is derived from the product of mass (in kilograms) and velocity (in meters per second).
Explanation:
To determine the proper unit for momentum using dimensional analysis, we first need to understand the physical definition of momentum. Momentum (π) is the product of an object's mass (m) and its velocity (v), thus having the formula π = m × v. According to SI units, mass is measured in kilograms (kg) and velocity in meters per second (m/s).
Performing dimensional analysis, we get:
Mass (m): [M] – SI unit: kg
Velocity (v): [LT−1] – SI Unit: m/s
Therefore, the dimensions of momentum are [M][LT−1] = [MLT−1]. When we multiply the units of mass and velocity, we get the unit of momentum as kilogram meters per second (kg·m/s), which is the proper unit for momentum.
What is the law of conservation of Machanical energy?
Final answer:
The law of conservation of mechanical energy states that the total mechanical energy (kinetic plus potential) in a closed system subjected to conservative forces remains constant, assuming no energy is lost via non-conservative forces like friction.
Explanation:
Law of Conservation of Mechanical Energy
The law of conservation of mechanical energy states that in a closed system where only conservative forces are acting, and in the absence of non-conservative forces such as friction or air resistance, the total mechanical energy of the system remains constant. Mechanical energy is the sum of the object's kinetic energy (energy due to motion) and potential energy (energy stored due to position). This implies that any loss in potential energy will result in an equal increase in kinetic energy, and vice versa, hence keeping the total energy unchanged.
As an example, consider a roller coaster. At the highest point, the car has maximum potential energy and minimum kinetic energy. As the car descends, potential energy decreases while kinetic energy increases. If we assume no energy loss to friction, the sum of potential and kinetic energies at any point will equal the total mechanical energy at the top of the first rise, illustrating the conservation of mechanical energy.
In mathematical terms, the law can be expressed as K + U = constant, where K represents kinetic energy and U represents potential energy. This conservation is also a consequence of the work-energy theorem when applied to conservative forces, leading to the understanding that the net work done is equal to the change in kinetic energy of the system.
Sonja is riding her bike. She takes her feet
off the pedals to freewheel down a hill.
Describe the energy transfers that take place as the bike travels down the hill.
Ignore friction and air resistance.
Answer:gravity
Explanation:
As Sonja coasts down the hill on her bike, the gravitational potential energy is converted into kinetic energy, which is the energy that increases her speed as she moves downhill.
When Sonja freewheels down the hill on her bike, the primary energy transfer is the conversion of gravitational potential energy to kinetic energy. At the top of the hill, the bike has a certain amount of potential energy due to its elevated position. As she moves downhill, this potential energy is converted into kinetic energy, which is the energy of motion, allowing the bike to increase in speed.
If we were not to ignore friction and air resistance, these factors would cause some of the kinetic energy to transform into thermal energy, due to the friction between the bike tires and the road as well as the air resistance against the rider and the bike.
However, since the question asks us to ignore these factors, we focus solely on the transformation of gravitational potential energy into kinetic energy as Sonja coasts down the hill.