Consider a father pushing a child on a playground merry-go-round. the system has a moment of inertia of 84.4 kg · m2. the father exerts a force on the merry-go-round perpendicular to its radius to achieve an angular acceleration of 4.44 rad/s2. (a) how long (in s) does it take the father to give the merry-go-round an angular velocity of 1.43 rad/s? (assume the merry-go-round is initially at rest.)
It takes 0.322 s to give the merry-go-round an angular velocity of 1.43 rad/s
[tex]\texttt{ }[/tex]
Further explanationCentripetal Acceleration can be formulated as follows:
[tex]\large {\boxed {a = \frac{ v^2 } { R } }[/tex]
a = Centripetal Acceleration ( m/s² )
v = Tangential Speed of Particle ( m/s )
R = Radius of Circular Motion ( m )
[tex]\texttt{ }[/tex]
Centripetal Force can be formulated as follows:
[tex]\large {\boxed {F = m \frac{ v^2 } { R } }[/tex]
F = Centripetal Force ( m/s² )
m = mass of Particle ( kg )
v = Tangential Speed of Particle ( m/s )
R = Radius of Circular Motion ( m )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
moment of inertia = I = 84.4 kg.m²
initial angular velocity = ωo = 0 rad/s
angular acceleration = α = 4.44 rad/s²
final angular velocity = ω = 1.43 rad/s
Asked:
time taken = t = ?
Solution:
[tex]\omega = \omega_o + \alpha t[/tex]
[tex]1.43 = 0 + 4.44t[/tex]
[tex]1.43 = 4.44t[/tex]
[tex]t = 1.43 \div 4.44[/tex]
[tex]t = 0.322 \texttt{ s}[/tex]
[tex]\texttt{ }[/tex]
Learn moreImpacts of Gravity : https://brainly.com/question/5330244Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454The Acceleration Due To Gravity : https://brainly.com/question/4189441[tex]\texttt{ }[/tex]
Answer detailsGrade: High School
Subject: Physics
Chapter: Circular Motion
[tex]\texttt{ }[/tex]
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
A ball is thrown horizontally from a cliff at a speed of 10 m/s. you predict that its speed 1 s later will be slightly greater than 14 m/s. your friend says it will be 10 m/s. show who is correct.
Answer:
Speed is slightly greater than 14 m/s.
Explanation:
The ball will under go projectile motion. The horizontal velocity remains constant while there would be increase in vertical velocity due to acceleration due to gravity in downward direction.
Using first equation of motion, after 1 s, vertical velocity will be:
v = u +at
v=0+(9.8 m/s²)(1 s) = 9.8 m/s
Horizontal velocity = 10 m/s
Net velocity:
[tex]V= \sqrt{(9.8)^2+(10)^2}=\sqrt{196.04}=14.001 m/s[/tex]
Speed is slightly greater than 14 m/s.
An energy pyramid illustrates that energy in the form of _____ is lost to the surroundings as it's passed from one organism to the next
what do you think will happen to dirt and rocks on the Mountainside when the ice melts
Final answer:
When the ice on a mountainside melts, dirt and rocks that were held in place by the ice become unstable and may move downhill, altering the landscape. Saturated soil can cause mud flows and contribute to erosion. Glaciers also play a significant role in sculpting landscapes by carrying rock and sediment as they move.
Explanation:
When ice on a mountainside melts, the dirt and rocks that were previously held in place by the ice may become less stable. Erosion processes, such as water runoff and gravity, can lead to increased movement of these materials. As the water from the melting ice saturates the mountain's soil and rock, it can trigger debris flows or mud flows. These events have the potential to transport large amounts of material downslope, often resulting in significant changes to the landscape. The movement of this material can lead to the formation of new features, such as valleys or depressions, and can also contribute to the reshaping or smoothing of existing mountainous terrain.
It's also worth noting that glaciers, which are large bodies of ice that move slowly over land, have historically been powerful agents of erosion. As they advance and retreat, glaciers grind down rocks and carry sediment far from its origin, which is evidence of their strong impact on shaping the landscapes.
Which of the following takes place in the combustion chamber of a gas turbine engine?
PLZ HELP: Which food items would be appropriate for a spacecraft? Check all that apply. A< brownie, B< dry salt and pepper, C
Suppose a supernova occurs in a star that initially had 10 solar masses. why would the likely end result not be a black hole?
A star with an initial mass of 10 solar masses will likely form a neutron star instead of a black hole after a supernova due to the mutual repulsion between densely packed neutrons that can support the core against its own gravitational weight.
Explanation:
Given a star with initial 10 solar masses that ends its life in a supernova explosion, it is more likely to form a neutron star rather than a black hole. Most stars end their life as white dwarfs or neutron stars. In the case of a very massive star, if the core's remaining mass is more than about three times that of the Sun, it may collapse into a black hole. However, if the mass is less than about three solar masses, the mutual repulsion between densely packed neutrons can support the core against its own weight, preventing it from becoming a black hole.
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A train accelerates from its metropolitan cruising speed of 22 m/s to its countryside cruising speed of 32 m/s. If it takes the train 142 seconds to do this, what is its acceleration?
10 m/s2
14.2 m/s2
4.4 m/s2
0.07 m/s2
Answer:
Acceleration of the train is 0.07 m/s²
Explanation:
Initial speed of the train, u = 22 m/s
Final speed of the train, v = 32 m/s
Time taken by the train to do the process is 142 seconds
We have to find the acceleration of the train. It is given by the rate of change of speed of the train i.e.
[tex]a=\dfrac{v-u}{t}[/tex]
[tex]a=\dfrac{32\ m/s-22\ m/s}{142\ s}[/tex]
[tex]a=0.07\ m/s^2[/tex]
So, the acceleration of the car is 0.07 m/s². Hence, the correct option is (d) 0.07 m/s²
Now assume that the stream flows east at 4.0 m/s. draw the vectors v⃗ w, representing the velocity of the stream, and v⃗ tot, representing the velocity of your rowboat relative to the stream bank. be sure to draw both vectors. draw v⃗ tot and v⃗ w starting at the tail and tip of v⃗ still respectively. the location, orientation and length of the vectors will be graded. each vector's length is displayed in meters per second.
Remember that the total velocity of the motion is the vector sum of the velocity you would have in still water and the stream. Always place the vectors carefully to be able to come up with an accurate sum vector.
A sphere mass m1 and a block of mass m2 are connected by a light cord that passes over a pulley. The radius of the pulley is R, and the mass of the thin rim is M.. The block slides on a frictionless, horizontal surface.
Derive an expression for the linear acceleration of the two objects
The expression for the linear expression of the two objects will be
[tex]a=\dfrac{m_1g}{m_2+m_1-M}[/tex]
What is acceleration?Acceleration is defined as the change of the velocity with the time. Acceleration is a vector quantity and is defined by both the magnitude and the direction.
The mass of sphere is m1 radius is R and mass m2 is connected by light chord.
Now by using free body diagram
The tension in the chord will be
[tex]m_1g-T_1=m_1a[/tex]
[tex]T_1=m_1(g-a)[/tex]
For tension T2 we will have
[tex]T_2=m_2a[/tex]
Now the torque will be
[tex]T_{net}=I\alpha[/tex]
[tex]T_2R-T_1R=I(\dfrac{a}{R})[/tex]
[tex]T_2R-T_1R=MR^2(\dfrac{a}{R})[/tex]
[tex]T_2-T_1=Ma[/tex]
[tex]m_2a-m_1(g-a)=Ma[/tex]
[tex]m_2a-m_1g+m_1a=Ma[/tex]
[tex]a(m_2+m_1-M)=m_1g[/tex]
[tex]a=\dfrac{m_1g}{m_2+m_1-M}[/tex]
Thus the expression for the linear expression of the two objects will be
[tex]a=\dfrac{m_1g}{m_2+m_1-M}[/tex]
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The board sandwiched between two other boards shown below weighs 87.5 n. if the coefficient of friction between the boards is 0.622, what must be the magnitude of the compression forces (assume horizontal) acting on both sides of the center board to keep it from slipping?
The compression forces acting on both sides of the center board = 70.338 N
Further explanationThe force acting on a system with static equilibrium is 0
[tex] \large {\boxed {\bold {\sum F = 0}} [/tex]
(forces acting as translational motion only, not including rotational forces)
[tex] \displaystyle \sum F_x = 0 \\\\\ sum F_y = 0 [/tex]
For objects undergoing rotation, the equilibrium must be met
[tex] \large {\boxed {\bold {\sum \tau = 0}} [/tex]
The force acting on the touchpad between the two fields is called the normal force (N)
While the frictional force arises because of 2 objects that come into direct contact, especially when there is motion between two objects that are in direct contact.
There are 2 friction forces
static friction: fs = us.N kinetic friction: fk = uk .N
The board sandwiched between two other boards will not fall if
a downward force = an upward force
or ΣFy = 0 (idle / equilibrium)
so that
A downward force = weight of the board sandwiched = 87.5 N
An upward force = arises from two static friction forces namely: us.N (N = reaction force of the compression forces=F) ---> us.F
then the force that works can be stated:
EFy = 0
W = 2fs
W = 2 (us.F)
87.5 N = 2 (0.622. F)
F = 70,338 N
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A force of 660 n stretches a certain spring a distance of 0.300 m. what is the potential energy of the spring when a 70.0 kg mass hangs vertically from it?
Sadi Carnot came up with a hypothetical heat engine that had the maximum possible efficiency. What discovery did Carnot make that helped him recognize how to create this "perfect" heat engine?
Answer:
The difference in the temperatures between the hot and cold reservoirs determined how well a heat engine would work
Explanation:
I got a 100% on my test
Two objects are moving at equal speed along a level, frictionless surface. the second object has twice the mass of the first object. they both slide up the same frictionless inclined plane. which object rises to a greater height?
Final answer:
Despite their different masses, two objects with equal speeds moving on a frictionless incline reach the same height because mechanical energy is conserved and potential energy at a given height is not dependent on mass.
Explanation:
In a scenario where two objects with different masses but equal speeds slide up a frictionless incline, the laws of physics tell us that both objects should reach an equivalent height. This is because the mechanical energy (kinetic plus potential energy) in a closed system without any external forces (like friction) is conserved. Since both objects start with the same kinetic energy (due to equal speeds) and potential energy is directly related to height (not mass), they should convert their kinetic energy into the same amount of potential energy, meaning they should rise to the same height before coming to a stop and sliding back down.
It's important to note that if there were friction or some other external force acting on the objects, the outcomes could be different as the mechanical energy would no longer be conserved in the same way, but in a frictionless situation, mass does not affect the height an object reaches if it starts with the same kinetic energy.
A girl stands on a sofa. identify the number of the action/reaction pairs of forces between the girl and the sofa.
Final answer:
There are at least two fundamental action-reaction pairs of forces when a girl stands on a sofa, including the force of gravity and the normal force, as well as any frictional forces if there is lateral movement.
Explanation:
Action-Reaction Pairs
In the scenario where a girl stands on a sofa, there are several action-reaction pairs of forces at play. According to Newton's third law, every action has an equal and opposite reaction. When the girl exerts a force on the sofa (due to her weight), the sofa exerts an equal and opposite force back onto the girl. This is one pair. Additionally, if the girl were to push on the sofa to stand up or adjust her position, the sofa would push back with an equal force in the opposite direction, forming another action-reaction pair.
The number of action-reaction pairs can vary based on what specific interactions are being considered. Generally, in this scenario, we consider at least two fundamental pairs: the force of gravity on the girl (action) and the normal force from the sofa on the girl (reaction), and if there's any lateral movement while standing, there would be a frictional force between the sofa and the girl's feet (action), and an equal and opposite frictional force from the girl's feet on the sofa (reaction).
It is friction that provides the force for a car to accelerate, so for high-performance cars the factor that limits acceleration isn't the engine; it's the tires. you may want to review ( pages 138 - 142) . part a for typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 60 mph? suppose that μs=1.00 and μk=0.80.
The shortest time in which a car could accelerate from 0 mph to 60 mph is [tex]13.7s[/tex].
Further explanation:
The opposite force acting on the body is known as frictional force. It always acts in the opposite direction of motion of body.
Concept used:
The force applied to a body to keep it at rest is known as the static friction force. It always acts opposite to the direction of motion of body. It is defined as the product of coefficient of friction and the normal force acting on the body.
The expression for the normal reaction of the body is given as.
[tex]N = mg[/tex]
The expression for the net force is given as.
[tex]{F_{net}} = ma[/tex] …… (1)
The expression for the static friction is given as.
[tex]{F_s} = {\mu _s}N[/tex]
The expression for the balanced forces is given as.
[tex]{F_{net}} = {F_s} - {F_r}[/tex]
Substitute[tex]{\mu _s}N[/tex] for [tex]{F_s}[/tex] and for[tex]{F_r}[/tex] in the above expression.
[tex]\begin{aligned}{F_{net}}&={\mu _s}N-{\mu _r}N\\&= \left( {{\mu _s} - {\mu _r}} \right)N \\ \end{aligned}[/tex]
Substitute [tex]mg[/tex] for [tex]N[/tex] in above expression.
[tex]{F_{net}}=\left({{\mu _s}-{\mu _r}}\right)\left( {mg}\right)[/tex] …… (2)
Compare equation (1) and (2) we get.
[tex]a=g\left({{\mu _s}-{\mu _r}}\right)[/tex] …… (3)
Here, [tex]a[/tex] is the acceleration of the body, g is the acceleration due to gravity, [tex]{\mu _s}[/tex] is the coefficient of static friction and is the coefficient of reactive force.
The expression for the first equation of motion is given as.
[tex]v = u + at[/tex]
Rearrange the above expression for time is given as.
[tex]\fbox{\begin\\t = \dfrac{{\left( {v - u} \right)}}{a}\end{minispace}}[/tex] …… (4)
Here, [tex]v[/tex] is the final velocity, [tex]u[/tex] is the initial velocity and [tex]t[/tex] is the time.
Substitute [tex]1[/tex] for [tex]{\mu _s}[/tex], [tex]0.8[/tex] for[tex]{\mu _r}[/tex] and [tex]9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}[/tex] for [tex]g[/tex] in equation (3).
[tex]\begin{aligned}a&=\left( {9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}}\right)\left( {1 - 0.8}\right)\\&=1.96\,{\text{m/}}{{\text{s}}^{\text{2}}} \\ \end{aligned}[/tex]
Substitute [tex]0\,{\text{mph}}[/tex] for [tex]u[/tex], [tex]60\,{\text{mph}}[/tex] for [tex]v[/tex] and [tex]1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}[/tex] for [tex]a[/tex] in equation (4).
[tex]\begin{aligned}t&=\frac{{\left( {60\,{\text{mph}}-0\,{\text{mph}}}\right)}}{{1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}}}\\&=\frac{{60\,{\text{mph}}\left( {\frac{{0.447\,{\text{m/s}}}}{{1\,{\text{mph}}}}} \right)}}{{1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}}}\\&= 13.7\,{\text{s}} \\ \end{aligned}[/tex]
Thus, the time required to accelerate a car is [tex]\fbox{\begin\\13.7\, {\text{s}}\end{minispace}}[/tex].
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Answer Details:
Grade: College
Subject: Physics
Chapter: Kinematics
Keywords:
Force, friction, Acceleration, acceleration due to gravity, normal, weight, mass, motion, sliding, sled, hill, inclined, plane, coefficient of friction, angle of inclination, 13.68 s, 13.69 s.
Final Answer:
So, under ideal conditions with the assumption of maximum static friction being available throughout the acceleration, the shortest time in which a typical car could accelerate from 0 to 60 mph on rubber-on-concrete would be approximately 2.734 seconds.
Explanation:
To solve this problem, we need to understand how the force of friction allows a car to accelerate and then apply the equations of motion to determine the shortest time it would take for the car to accelerate from 0 to 60 miles per hour (mph).
First, we need to define our variables and constants:
- The static friction coefficient between rubber and concrete, μs, which is 1.00. This is the factor that will limit our acceleration since it represents the maximum frictional force that can be exerted before sliding begins.
- The acceleration due to gravity, g, which is 9.81 m/s^2.
- The initial speed of the car, 0 mph, which needs to be converted to meters per second (m/s).
- The final speed of the car, 60 mph, which also needs to be converted to meters per second.
The force of static friction (f_friction) responsible for the acceleration can be calculated by multiplying the static friction coefficient (μs) with the normal force (N). The normal force, in this case, is equal to the weight of the car, which is the mass (m) times the acceleration due to gravity (g). Since we are looking for the highest possible acceleration, we can assume that the force of static friction is at its maximum value.
f_friction = μs * m * g
However, we don't need to know the mass of the car because it will cancel out in the equation of motion. The maximum possible acceleration (a_max) happens when the force of static friction is at its highest, and it can be calculated using:
a_max = f_friction / m = μs * g
Now we have the maximum possible acceleration the tires can provide on concrete, which is:
a_max = 1.00 * 9.81 m/s^2
a_max = 9.81 m/s^2
Next, let's convert the final velocity from mph to m/s:
v_final(mph) = 60 mph
v_final(m/s) = v_final(mph) * 0.44704 (conversion factor from mph to m/s)
v_final(m/s) = 60 * 0.44704
v_final(m/s) ≈ 26.8224 m/s
With the initial velocity (v_initial) being 0 m/s (since we start from rest), we can use one of the kinematic equations to find the time (t):
v_final = v_initial + a_max * t
26.8224 m/s = 0 m/s + 9.81 m/s^2 * t
Solving for t, we get:
t = v_final / a_max
t ≈ 26.8224 m/s / 9.81 m/s^2
t ≈ 2.734 seconds
So, under ideal conditions with the assumption of maximum static friction being available throughout the acceleration, the shortest time in which a typical car could accelerate from 0 to 60 mph on rubber-on-concrete would be approximately 2.734 seconds.
While driving your car on a level road at 60.0 mph, the traffic ahead of you comes to a sudden stop. you apply your brakes in a panic, causing them to lock. your car skids for 57.0 m before hitting the car in front of you. if µk = 0.550 for your tires on the road, find the speed of your car as it collides with the other car?
First let us calculate the acceleration of the car.
The net force is equivalent to the frictional force:
m a = µk m g
a = µk g
a = 0.550 * 9.8 m/s^2
a = 5.39 m/s^2 (negative direction) = -5.39 m/s^2
Then we use the equation:
v^2 = vi^2 + 2 a d
where v is final speed or velocity, vi is initial speed = 60 mph = 26.8224 m/s, d is distance
v^2 = (26.8224 m/s)^2 + 2 (-5.39 m/s^2) * 57 m
v^2 = 104.98 m^2/s^2
v = 10.25 m/s (ANSWER)
A can of sardines is made to move along an x axis from x = 0.47 m to x = 1.20 m by a force with a magnitude given by F = exp(–8x), with x in meters and F in newtons. (Here exp is the exponential function.) How much work is done on the can by the force?
A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. if the disk starts from rest and is then brought in contact with a spinning rubber wheel, we observe that the disk gradually begins to rotate too. if after 22 s of contact with this spinning rubber wheel, the disk has an angular velocity of 3.0 rad/s, find the average angular acceleration that the disk experiences. (assume the positive direction is in the initial direction of rotation of the disk. indicate the direction with the sign of your answer.)
in texas the speed limited in a/an is 30 mph
In Texas, the speed limit in urban districts is generally set at 30 mph unless otherwise posted. This means that unless there are signs indicating a different speed limit, drivers are expected to adhere to a maximum speed of 30 miles per hour when traveling through urban areas. Therefore, the correct answer is A. 30 mph.
The rationale behind setting a default speed limit for urban districts is to promote safety for both motorists and pedestrians. Urban areas typically have higher population densities, increased pedestrian activity, and more complex traffic patterns compared to rural or suburban areas. As a result, lower speed limits help reduce the risk of accidents, particularly those involving pedestrians and cyclists.
By setting a default speed limit of 30 mph in urban districts, Texas law aims to create safer environments for all road users. However, it's essential for drivers to remain vigilant and observant of posted speed limit signs, as speed limits may vary depending on factors such as road conditions, proximity to schools or residential areas, and construction zones.
Overall, the default speed limit of 30 mph in urban districts reflects a balance between ensuring efficient traffic flow and prioritizing the safety of all individuals on the road. Therefore, the correct answer is A. 30 mph.
The complete question is:
In Texas, the speed limit in urban districts is _______ unless otherwise posted.
A. 30 mph
B. 50 mph
C. 40 mph
D. 25 mph
A satellite, moving in an elliptical orbit, is 360 km above earth's surface at its farthest point and 180 km above at its closest point. calculate (a) the semimajor axis and (b) the eccentricity of the orbit.
The semimajor axis is equal to 270 Km. The eccentricity of the orbit is 0.33 Km.
What is an elliptical orbit?An elliptic orbit or elliptical orbit can be described as a Kepler orbit with an eccentricity of less than 1. It is a circular orbit with an eccentricity equal to 0. It is a Kepler orbit with an eccentricity greater than 0 and less than 1 and a Kepler's orbit with negative energy. The radial elliptic orbit has an eccentricity equal to 1.
Given the satellite, moving in an elliptical orbit has the farthest point from the above earth's surface, [tex]R_a[/tex] = 360 Km
The closest point from the above earth's surface, [tex]R_p[/tex] = 180 Km
Semi-major axis can be calculated as , [tex]{\displaystyle a = \frac{R_a+R_p}{2}[/tex]
[tex]{\displaystyle a = \frac{360 + 180}{2}[/tex]
a = 270 km
The eccentricity of the elliptical orbit, we can calculate as shown below:
[tex]{\displaystyle e = \frac{a- R_p}{a}[/tex]
e = (270 - 180)/270
e = 1/3
e = 0.33 km
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Manny walked a total of 3 miles. The reference point used to calculate the total distance that he walked was the same as the ending point. Which describes where Manny most likely walked? from the bottom of a hill to the top on a circular nature trail on a sidewalk from his house to the mall from the beginning of a straight track to the end
As per the statement, Manny walks about 3 miles and the reference point for calculating the distance is the same as the starting point.
Thus manny walked on a circular nature trail. As the starting point is equal to the ending point and the bottom of the hill is a reference point and the top. So manny is in a circular pathway.Hence the option B is correct.
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A force of 25 N acts on an object at an angle of 30 degrees above the horizontal. How much work does the force do if the object slides 3 m?
The force does 195 Joules of work on the object.
Explanation:To calculate the work done by a force, we use the formula:
Work = Force x Distance x cos(theta)
Given that the force is 25 N, the angle is 30 degrees, and the distance is 3 m, we can substitute these values into the formula to calculate the work:
Work = 25 N x 3 m x cos(30 degrees) = 195 J
Therefore, the force does 195 Joules of work on the object.
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Alcohols are organic compounds that contain a. carbon and oxygen only. c. carbon, oxygen, and hydrogen. b. carbon and hydrogen only. d. carbon, nitrogen, and hydrogen.
Answer: Option (c) is the correct answer.
Explanation:
Compounds which contain carbon and hydrogen atoms are known as organic compounds.
As general chemical formula of alcohols is R-OH, where R = any alkyl or aryl group.
For example, [tex]CH_{2}CH_{2}OH[/tex] is known as ethanol and it is an alcohol as it contains the functional group "-OH".
So, alcohols contains elements carbon, hydrogen and oxygen.
Thus, we can conclude that alcohols are organic compounds that contain carbon, oxygen, and hydrogen.
A spring that has a spring constant of 1400 N/m is stretched to a length of 2.5 m. If the normal length of the spring is 1.0 m, how much elastic potential energy is stored in the spring? 700 J 1050 J 1575 J 4375 J
Which of the following statements proves that scientific knowledge changed due to the discovery of the fossil of a hadrosaur in North Dakota?
Hadrosaurs were better runners than earlier thought.
Hadrosaurs had no pattern on their skin, which was not expected.
The length of the hadrosaur was shorter than previously thought.
The muscular structure of the hadrosaur was less developed than expected.
A 1490-kilogram truck moving with a speed of 27.0 m/s runs into the rear end of a 1280-kilogram stationary car. if the collision is completely inelastic, how much kinetic energy is lost in the collision?
The loss in kinetic energy in an inelastic collision is equal to 251104 J.
What is law of conservation of momentum?According to the law of conservation of linear momentum, the sum of the momentum before and after an inelastic collision must be equal.
m₁u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
where m₁ and m₂ is the mass of the collided bodies, u₁ & u₂ are their initial speed while v₁ & v₂ is their final speed.
Given the initial velocity of the truck is v₁ = 27 m/s and the other car is at rest, u₂ = 0 m/s.
The mass of the truck, m₁ = 1490 Kg
The mass of the stationary car, m₂ = 1280 Kg
From the law of conservation of momentum, find the final speed after a collision:
m₁ u₁ + m₂ u₂ = (m₁ + m₂)v'
1490 × 27 + 1280 ×0 = (1490 + 1280) v'
v' = 14.52 m/s
The loss in the kinetic energy = [tex]=\frac{1}{2} mv_1^2-\frac{1}{2} (m_1+m_2)^2v^'^2[/tex]
[tex]==\frac{1}{2} \times 1490\times(27)^2-\frac{1}{2} (2770)^2(14.52)^2[/tex]
[tex]= 543105 -292000\\=251104 J[/tex]
Therefore, the loss in the kinetic energy in the collision is equal to 251104 J.
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WHO EVER THAT CAN ANSWER THIS GETS 17 POINTS
1. Research how cars or planes have been designed to have less mass.
2. How is the balance between
strength and mass resolved when
designing cars or planes?
To make cars and airplanes lighter, engineers use materials with high strength-to-weight ratios and apply aerodynamic principles to reduce drag. The balance of strength versus mass is resolved through materials selection and careful design optimization, including computer simulations and wind tunnel tests to create vehicles that are strong, lightweight, and efficient.
When designing cars or airplanes, the challenge is to reduce the mass of the vehicle while maintaining structural integrity. One way to achieve a lighter car is to incorporate plastics instead of metal in parts of its construction. For airplanes, advanced composite materials such as carbon fiber are often used because of their strength-to-weight ratios. Aerodynamics play a critical role in this process, as reducing drag through aerodynamic shaping can not only decrease fuel consumption but also reduce the required structural mass.
The balance between strength and mass is resolved through the use of advanced materials and design strategies. Modern design approaches involve analyzing aerodynamic forces and optimizing the shape and structures to endure these forces. With the help of computer simulations and wind tunnel testing, engineers can fine-tune designs to achieve the desired balance. The selection of materials follows a criterion that ensures they are lightweight yet able to withstand the high stresses experienced during operation. Often, the design includes failsafes that account for the worst expected loads.
Ultimately, the goal is to meet specific design objectives that include performance metrics like range, payload capacity, and fuel efficiency. Designers look at comparator aircraft or vehicles and use their data as references for optimizing wing loading, thrust-to-weight ratio, and other design parameters. Thus, the optimal design is often a trade-off between various competing factors including mass, strength, and aerodynamic efficiency.
A daredevil decides to jump a canyon of width 8.88 m. to do so, he drives a motorcycle up an incline sloped at an angle of 22.5 ◦ . the acceleration of gravity is 9.8 m/s 2 . what minimum speed must he have in order to clear the canyon? answer in units of m/s.
Final Answer:
The daredevil must have a minimum speed of approximately 14.7 m/s to clear the canyon.
Explanation:
To clear the canyon, the daredevil's vertical displacement at the edge of the canyon must be equal to the width of the canyon. Using the kinematic equation for vertical motion [tex]\( y = v_0t + \frac{1}{2}gt^2 \)[/tex], where y is the vertical displacement, [tex]\( v_0 \)[/tex] is the initial vertical velocity, g is the acceleration due to gravity, and t is the time of flight, and solving for [tex]\( v_0 \)[/tex], we get [tex]\( v_0 = \sqrt{2gy} \)[/tex]. Substituting the given values [tex]\( g = 9.8 \, \text{m/s}^2 \) and \( y = 8.88 \, \text{m} \)[/tex], we find [tex]\( v_0 \approx 14.7 \, \text{m/s} \)[/tex], which is the minimum speed required to clear the canyon.