A barrel ride at an amusement park starts from rest and speeds up to 0.520 rev/sec in 7.26 s. What is the angular acceleration during that time? (Unit = rad/s^2)

Answer:

Upward

Explanation:

For charged particles immersed in an electric field:

- if the particle is positively charged, the direction of the force is the same as the direction of the electric field

- if the particle is negatively charged, the direction of the force is opposite to the direction of the electric field

In this problem, we have an electron - so a negatively charged particle - so the direction of the force is opposite to that of the electric field.

Since the electric field is directed downward, therefore, the electric force on the electron will be upward.

Answer:

The power of the motor is 153000 watts.

Explanation:

It is given that,

Mass of the car, m = 1700 kg

Initially, it is at rest, u = 0

Final velocity of the car, v = 30 m/s

Time taken, t = 5 s

We need to find the power of a motor. Work done per unit time is called power of the motor. We know that the change in kinetic energy is equal to the work done i.e.

[tex]P=\dfrac{W}{t}=\dfrac{\Delta E}{t}[/tex]

[tex]P=\dfrac{\dfrac{1}{2}mv^2}{t}[/tex]

[tex]P=\dfrac{\dfrac{1}{2}\times 1700\ kg\times (30\ m/s)^2}{5\ s}[/tex]

P = 153000 watts

So, the power of the motor is 153000 watts. Hence, this is the required solution.

Answer:

The current in the heater is 12.5 A

Explanation:

It is given that,

Power of electric heater, P₁ = 1400 W

Power of toaster, P₂ = 1150 W

Power of electric grill, P₃ = 1560 W

All three appliances are connected in parallel across a 112 V emf source. We need to find the current in the heater. We know that in parallel combination of resistors the current flowing in every branch of resistor divides while the voltage is same.

Electric power, [tex]P_1=V\times I_1[/tex]

[tex]I_1=\dfrac{P_1}{V}[/tex]

[tex]I_1=\dfrac{1400\ W}{112\ V}[/tex]

[tex]I_1=12.5\ A[/tex]

So, the current in the heater is 12.5 A. Hence, this is the required solution.  

(a) 252 N, opposite to the applied force

There are two forces acting on the refrigerator in the horizontal direction:

- the pushing force of 252 N, F, forward

- the frictional force, Ff, pulling backward

In this case, the refrigerator is not moving: this means that its acceleration is zero. According to Newton's second law, this also means that the net force acting on the refrigerator is also zero:

[tex]\sum F = ma = 0[/tex]

So we have

[tex]F-F_f = 0[/tex]

which means that the frictional force is equal in magnitude to the pushing force:

[tex]F_f = F = 252 N[/tex]

and the direction is opposite to the pushing force.

(b) 334.8 N

The force that must be applied to the refrigerator to make it moving is equal to the maximum force of friction, which is given by:

[tex]F_{max} = \mu mg[/tex]

where

[tex]\mu = 0.61[/tex] is the coefficient of static friction

m = 56 kg is the mass of the refrigerator

g = 9.8 m/s^2 is the acceleration of gravity

Substituting:

F_max = (0.61)(56 kg)(9.8 m/s^2)=334.8 N

The force that will move the object is 83 N in the negative x direction.

The frictional force is the force that opposes motion. The force of friction acts in the opposite direction to the force that is moving the object. Now we can obtain the frictional force from;

μs = F/mg

F = μsmg = 0.61 * 56 kg * 9.8 m/s^2 = 335 N (positive  direction)

Secondly;

ma = F - Ff

Where;

ma = resultant force

F = moving force

Ff = frictional force

Now we need to find the net force ma

ma = 252 N - 335 N

ma = -83 N

The force that will move the object is 83 N in the negative x direction.

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Answer:

335°C

Explanation:

Heat gained or lost is:

q = m C ΔT

where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

Heat gained by the water = heat lost by the copper

mw Cw ΔTw = mc Cc ΔTc

The water and copper reach the same final temperature, so:

mw Cw (T - Tw) = mc Cc (Tc - T)

Given:

mw = 390 g

Cw = 4.186 J/g/°C

Tw = 22.6°C

mc = 248 g

Cc = 0.386 J/g/°C

T = 39.9°C

Find: Tc

(390) (4.186) (39.9 - 22.6) = (248) (0.386) (Tc - 39.9)

Tc = 335

Data obtained from the question

Mass of copper (M꜀) = 248 g

Volume of water  = 390 mL

Density of water = 1 g/mL

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

Determination of the mass of water

Volume of water = 390 mL

Density of water = 1 g/mL

[tex]Density = \frac{mass}{volume}\\\\1 = \frac{mass}{390}[/tex]

Cross multiply

[tex]Mass = 1 * 390[/tex]

Determination the initial temperature of the copper.

Mass of copper (M꜀) = 248 g

Mass of water (Mᵥᵥ) = 390 g

Initial temperature of water (Tᵥᵥ) = 22.6 °C

Equilibrium temperature (Tₑ) = 39.9 °C

1. Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC

2. Specific heat capacity of copper (C꜀) = 0.385 J/gºC

Heat lost by copper = heat gained by water

[tex]Q_{c} = Q_{w} \\ \ M_{c} C_{c}(T_{c}-T_{e}) = M_{w} C_{w}(T_{e}-T_{w})\\248* 0.385(T_{c}-39.9) = 390*4.184(39.9-22.6)\\95.48(T_{c}-39.9) = 1631.76*17.3\\95.48(T_{c}-39.9) = 28229.448[/tex]

Divide both side by 95.48

[tex]T_{c} - 39.9 = \frac{28229.448}{95.48}\\T_{c} - 39.9 = 295.658[/tex]

Collect like terms

[tex]T_{c} = 295.658 + 39.9[/tex]

Therefore, the initial temperature of the piece of copper is 335.6 °C.

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Answer:

No, it is not correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source.

Explanation:

While Doppler Effect is due to motion of the source or observer but it is not the apparent change in the speed of the wave. The speed of the wave remains the same. It is the wavelength and frequency of the waves that change in Doppler Effect when there is a relative motion between source and observer.

The Doppler Effect is the change in frequency, not speed, of a wave due to the relative motion between the source and observer.

It would not be correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source. The Doppler Effect actually refers to the apparent change in the frequency of a wave as a result of the relative motion between the source of the wave and the observer. While the speed of the wave itself remains constant, the wavelength experienced by the observer can either compress or stretch depending on whether the source is moving towards or away from them, thereby changing its perceived frequency.

The time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]

The formula for calculating the average speed is expressed according to the formula:

[tex]Speed= \frac{distance}{time}[/tex]

Given the speed of light as [tex]3.0 \times 10^8m/s[/tex]

Distance from earth to the sum is [tex]149.6\times 10^9m[/tex]

Substitute the given parameters into the formula to get the time "t"

[tex]t=\frac{d}{t} \\t=\frac{149.6\times10^9m}{3.0\times10^8}\\t=49.87\times 10\\t =498.7secs[/tex]

Hence the time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]

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Answer:

Option (a)

Explanation:

If a body is thrown upwards, it's velocity goes on decreasing with constant rate. It is because an acceleration is acting on the body which is equal to acceleration due to gravity and acting downwards. The value of acceleration due to gravity is constant and always acting downwards.

Explanation and answer:

This problem is best answered by drawing a figure as a first step.

ABC is the scaffold.

A downward force of 500N is applied downwards at 1m from end A.

The weight of 800N is exerted by the scaffold uniformly distributed between A & C.

At A and C, ropes are attached to support the load.

Let Fc=tension in rope passing through C.

Take moments about A:

Fc = (500N * 1m +800N*(3+1)/2m / 4m

    = (500 Nm + 1600Nm) / 4m

    = 2100 Nm / 4m

   = 525 N

Probably not. The elevator has security system just like any device. It will automatically trigger breaks in case it detects some sort of free fall.

Person inside free falling elevator could experience 0G or no gravity effect something similar to what astronauts experience in earth's orbit.

The only damage that could happen to you is when the breaks are released you won't feel 0G anymore and fall about 4ft to the floor of the elevator.

Hope this helps.

r3t40

Answer:

Number of electrons, [tex]n=2.7\times 10^{19}[/tex]

Explanation:

It is given that,

Charge, q = 4.33 C

We need to find the number of electrons that make 4.33 C of charge. According to quantization of charge as :

[tex]q=ne[/tex]

n = number of electrons

e = electron's charge

[tex]n=\dfrac{q}{e}[/tex]

[tex]n=\dfrac{4.33\ C}{1.6\times 10^{-19}\ C}[/tex]

[tex]n=2.7\times 10^{19}[/tex]

So, the number of electrons are [tex]2.7\times 10^{19}[/tex] Hence, this is the required solution.  

Answer:

The length of the string is 0.051 meters

Explanation:

It is given that,

Tension in the string, T = 240 N

Mass of the string, m = 0.086 kg

Speed of the wave, v = 12 m/s

The speed of the wave on the string is given by :

[tex]v=\sqrt{\dfrac{T}{M}}[/tex]

M is the mass per unit length of the string i.e. M = m/l.......(1)

So, [tex]M=\dfrac{T}{v^2}[/tex]

[tex]M=\dfrac{240\ N}{(12\ m/s)^2}[/tex]

M = 1.67 kg/m

The length of the string can be calculated using equation (1) :

[tex]l=\dfrac{m}{M}[/tex]

[tex]l=\dfrac{0.086\ kg}{1.67\ kg/m}[/tex]

l = 0.051 m

So, the length of the string is 0.051 meters. Hence, this is the required solution.

Explanation:

We'll need two equations.

v² = v₀² + 2a(x - x₀)

where v is the final velocity, v₀ is the initial velocity, a is the acceleration, x is the final position, and x₀ is the initial position.

x = x₀ + ½ (v + v₀)t

where t is time.

Given:

v = 47.5 m/s

v₀ = 34.3 m/s

x - x₀ = 40100 m

Find: a and t

(47.5)² = (34.3)² + 2a(40100)

a = 0.0135 m/s²

40100 = ½ (47.5 + 34.3)t

t = 980 s

Answer:

i believe that it is d

Explanation:

In a super heater, the temperature of the steam rises while the pressure remains constant. This process helps to remove the last traces of moisture from the saturated steam.

In a super heater, the conclusion is that option (C) pressure remains constant and temperature rises is the correct choice. A super heater is a device used in a steam power plant to increase the temperature of the steam, above its saturation temperature. The function of the super heater is to remove the last traces of moisture (1 to 2%) from the saturated steam and to increase its temperature above the saturation temperature. The pressure, however, remains constant during this process because the super heater operates at the same pressure as the boiler.

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Answer:

The current will be 3.23 A.

Explanation:

Given that,

Current I = 4.68 A

Voltage V = 220 volt

We need to calculate the resistance

Using ohm's law

[tex]V = I R[/tex]

[tex]R = \dfrac{V}{I}[/tex]

Where,

V = voltage

I = current

R = resistance

Put the value into the formula

[tex]R = \dfrac{220}{4.68}[/tex]

[tex]R = 47\ \Omega[/tex]

We need to calculate the current

If the voltage drops by 31%

Voltage will be

[tex]V'=V-V\times31%[/tex]

[tex]V'=220-220\times\dfrac{31}{100}[/tex]

[tex]V'=151.8\ volt[/tex]

Now, the current will be

[tex]I = \dfrac{151.8}{47}[/tex]

[tex]I=3.23\ A[/tex]

Hence, The current will be 3.23 A.

Answer:

The correct answer is :A and C

Explanation:

According to the rule

1- Zeroes at the beginning of a number are never significant.

2- Zeroes at the end of a number are significant if there is a decimal point.

(a) 0.00012 s and 12000 s

0.00012 has 2 significant figure and 12000 has 2 significant figures

(b) 11.0 m and 11.00 m

11.0 has 3 significant figures and 11.00 has 4 significant figure.

(c)  0.0250 m and 0.205

0.0250 has 3 significant figure and 0.250 has 3 significant figures

(d) 250.0 L and 2.5×10−2L

250.0 has 4 significant figures and 2.5x10−2 has 2 sig figures.

So (a) and (c) pairs have same number of sig figures.

Final answer:

The pair out of the provided options that contains the same number of significant figures is 0.0250 m and 0.205 m, both with three significant figures.

Explanation:

When comparing significant figures in different numbers, we must apply the rules for determining the number of significant figures to each number.

0.00012 s has two significant figures (the leading zeros are not significant).

12000 s likely has two significant figures (unless further decimal places are indicated or if it's written in scientific notation, such as 1.2×10⁴ which would have three significant figures).

11.0 m and 11.00 m have three and four significant figures respectively (trailing zeros after a decimal are significant).

0.0250 m has three significant figures (leading zeros are not significant, but trailing zeros after a decimal are).

0.205 m has three significant figures (leading zeros are not significant).

250.0 L has four significant figures (trailing zeros after a decimal are significant).

2.5×10⁻² L has two significant figures (in scientific notation, all digits are significant).

Therefore, the pairs that contain the same number of significant figures are 0.0250 m and 0.205 m, both with three significant figures.

Answer:

part a)

[tex]U = 2\times 10^9 J[/tex]

Part b)

[tex]m = 5.6 \times 10^3 kg[/tex]

Part c)

Huge damage will be there in tree

Explanation:

Part a)

Energy loss due to charge flow through given potential difference is given as

[tex]U = qV[/tex]

now plug in all the values in it

[tex]U = (20 C)(1.00 \times 10^2 \times 10^6 V)[/tex]

[tex]U = 2\times 10^9 J[/tex]

Part b)

Now this energy is used to raise the temperature of water from 15 degree C to boiling point

So here we will have

[tex]Q = ms\Delta T[/tex]

[tex]2 \times 10^9 = m(4186)(100 - 15)[/tex]

[tex]m = 5.6 \times 10^3 kg [/tex]

Part c)

Since in part b) we can say its a huge amount of water that will boil due to the amount of energy that strikes to the tree.

So it will make huge damage to the tree

Final answer:

A lightning bolt moving 20.0 C of charge through a potential difference of 1.00 × 10² MV dissipates 2.00 × 10¹ joules of energy. This energy can boil a significant mass of water, demonstrating the power of lightning. The rapid boiling of sap and expansion of steam can cause the tree to explosively splinter.

Explanation:

Understanding the Physics of a Lightning Strike on a Tree

A lightning bolt striking a tree involves complex physical phenomena, including the movement of charge and the dissipation of significant amounts of energy. When a lightning bolt with 20.0 C of charge passes through a potential difference of 1.00 × 10² MV, we can calculate the energy dissipated using the relationship between charge, potential difference, and energy.

(a) Calculating Dissipated Energy:

The energy dissipated can be calculated using the formula E = QV, where E is the energy in joules, Q is the charge in coulombs, and V is the potential difference in volts. Given the charge (20.0 C) and the potential difference (1.00 × 10² MV or 1.00 × 10¸ V), the energy dissipated is 2.00 × 10¹ joules (or 2 billion joules).

(b) Heating and Boiling Water with This Energy:

To determine what mass of water could be raised from 15°C to the boiling point and then boiled, we need to consider the specific heat capacity of water and the latent heat of vaporization. However, without diving into specific calculations here, it's clear that the energy amount is sufficient to boil a significant mass of water, showcasing the tremendous power of lightning.

(c) Potential Damage to the Tree:

The sudden energy release and the boiling of sap inside the tree can cause severe damage. The rapid expansion of steam may result in the explosive splintering of the tree trunk, a common effect seen in trees struck by lightning.

Answer:

The speed of the satellite is 7809.52 m/s        

Explanation:

It is given that,

Radius of Earth, [tex]r=6.38\times 10^6\ m[/tex]

Mass of earth, [tex]M=5.98\times 10^{24}\ kg[/tex]

A satellite moves in a circular orbit a distance of, [tex]d=1.6\times 10^5\ m[/tex]  above Earth's surface.

We need to find the speed of the satellite. It is given by :

[tex]v=\sqrt{\dfrac{GM}{R}}[/tex]

R = r + d

[tex]R=(6.38\times 10^6\ m+1.6\times 10^5\ m)=6540000\ m[/tex]

So, [tex]v=\sqrt{\dfrac{6.67\times 10^{-11}\ Nm^2/kg^2\times 5.98\times 10^{24}\ kg}{6540000\ m}}[/tex]

v = 7809.52 m/s

So, the speed of the satellite is 7809.52 m/s. Hence, this is the required solution.

Answer:

The period and frequency of this pendulum are 2.457 s and 0.407 Hz.

Explanation:

Given that,

Length = 1.5 m

Angle = 20°

We need to calculate the period

Using formula of period

[tex]T = 2\pi\sqrt{\dfrac{L}{g}}[/tex]

Where, T = time period

g = acceleration due to gravity

l = length

Put the value into the formula

[tex]T=2\times3.14\sqrt{\dfrac{1.5}{9.8}}[/tex]

[tex]T=2.457\ sec[/tex]

We need to calculate the frequency

[tex]T = \dfrac{1}{f}[/tex]

[tex]f=\dfrac{1}{T}[/tex]

Put the value of T

[tex]f=\dfrac{1}{2.457}[/tex]

[tex]f =0.407\ Hz[/tex]

Hence, The period and frequency of this pendulum are 2.457 s and 0.407 Hz.

Answer:

The terminal voltage will be 5.99 volt.

(d) is correct option.

Explanation:

Given that,

Voltage = 6.00

Internal r= 0.8322 ohm

Total resistance R =7380 ohm

We need to calculate the current

Using current formula

[tex]I=\dfrac{V}{R+r}[/tex]

Put the value into the formula

[tex]I = \dfrac{6}{7380+0.8322}[/tex]

[tex]I=0.000812\ A[/tex]

We need to calculate the voltage drop due to internal resistance

[tex]V' = Ir[/tex]

[tex]V'=0.000812\times0.8322[/tex]

[tex]V'=0.00067\ volt[/tex]

Now, The terminal voltage will be

[tex]V''=6-V'[/tex]

[tex]V''=6-0.00067[/tex]

[tex]V''=5.99\ volt[/tex]

Hence, The terminal voltage will be 5.99 volt,

Answer:

[tex]1.22\cdot 10^3 L[/tex]

Explanation:

We can solve the problem by using Charle's law, which states that for a gas kept at constant pressure, the volume of the gas is directly proportional to its temperature:

[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]

where here we have

[tex]V_1 = 1.09\cdot 10^3 L[/tex] is the initial volume

[tex]T_1 = 23^{\circ}+ 273 = 296 K[/tex] is the initial temperature

[tex]V_2[/tex] is the final volume

[tex]T_2 = 59^{\circ}+ 273 =332 K[/tex] is the final temperature

Solving for V2, we find

[tex]V_2 = \frac{V_1 T_2}{T_1}=\frac{(1.09 \cdot 10^3 L)(332 K)}{296 K}=1.22\cdot 10^3 L[/tex]

Explanation:

If the distance between the bottom of the ladder and the wall is x, then:

cos θ = x / 10

Taking derivative with respect to time:

-sin θ dθ/dt = 1/10 dx/dt

Substituting for θ:

-sin (acos(x / 10)) dθ/dt = 1/10 dx/dt

Given that x = 6 and dx/dt = 1.1:

-sin (acos(6/10)) dθ/dt = 1/10 (1.1)

-0.8 dθ/dt = 0.11

dθ/dt = -0.1375

The angle is decreasing at 0.1375 rad/s.

Answer:

The time is 5.21 s.

Explanation:

Given that,

Force F = 646 N

Mass m = 82 kg

Velocity v = 41 m/s

We need to calculate the acceleration

Using formula of force

F= ma

[tex]a = \dfrac{F}{m}[/tex]

[tex]a = \dfrac{646}{82}[/tex]

[tex]a =7.87\ m/s^2[/tex]

We need to calculate the time

Now, using equation of motion

[tex]v = u+at[/tex]

[tex]41=0+7.87 t[/tex]

[tex]t = \dfrac{41}{7.87}[/tex]

[tex]t = 5.21\ s[/tex]

Hence, The time is 5.21 s.

Answer:

The magnetic field produced by a long straight current-carrying wire is directly proportional to the current in the wire and inversely proportional to the distance from the wire.

Explanation:

The magnetic field produced by a long straight current-carrying wire is given by :

[tex]B=\dfrac{\mu_0I}{2\pi d}[/tex]............(1)

Where

[tex]\mu_o[/tex] = permeability of free space, [tex]\mu_o=4\pi\times 10^{-7}\ T-m/A[/tex]

I = current flowing in the wire

d = distance from wire

From equation (1), it is clear that the magnetic field produced by a long straight current-carrying wire is directly proportional to the current flowing and inversely proportional to the distance from the wire. So, the correct option is (d).

The magnetic field produced by a long straight current-carrying wire is proportional to the current in the wire and inversely proportional to the distance from the wire, demonstrated by Ampere's Law and the right-hand rule.

The magnetic field produced by a long straight current-carrying wire is D) proportional to the current in the wire and inversely proportional to the distance from the wire. This relationship is described by Ampere's Law and the formula B = μI/2πr, where B is the magnetic field strength, μ is the permeability of free space, I is the current in the wire, and r is the distance from the wire. This suggests that as the current increases, the magnetic field strength increases, and as the distance from the wire increases, the magnetic field strength decreases.

Furthermore, the direction of the magnetic field is given by the right-hand rule. If you point the thumb of your right hand in the direction of the current, your fingers will curl in the direction of the magnetic field loops, which form concentric circles around the wire.

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Answer:

The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].

Explanation:

Given that,

Current = 7.2 A

Time = 4.7 hours

We need to calculate the charge

The charge is the product of current and time.

Using formula of charge

[tex]Q=it[/tex]

Where, Q = charge

i = current

t = time

Put the value into the formula

[tex]Q=7.2\times4.7\times3600[/tex]

[tex]Q=1.22\times10^{5}\ C[/tex]

Hence, The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].

The minimum speed of an object in simple harmonic motion occurs when it is at the equilibrium point. Hence the correct answer is option B

In simple harmonic motion, the minimum speed of an object occurs when it is at the equilibrium point. The equilibrium position is where the object would naturally rest in the absence of force. When the object is at the equilibrium point, it has zero acceleration and the speed is at its minimum.

Hence the correct answer is option B

Answer:

The ball to hit the ground in 0.53 s.

Explanation:

Given that,

Height = 1.4 m

Time t = 0.53 s

Initial speed = 35 m/s

We need to calculate the time when the ball to hit the ground

Using equation of motion

[tex]s_{y}=u_{y}t-\dfrac{1}{2}gt^2+h_{0}[/tex]

Where, s= vertical height

u= vertical velocity

t = time

h = height

Put the value in equation

[tex]0=0-\dfrac{1}{2}\times9.8\times t^2+1.4[/tex]

[tex]t^2=\dfrac{1.4}{4.9}[/tex]

[tex]t=\sqrt{\dfrac{1.4}{4.9}}[/tex]

[tex]t=0.53\ s[/tex]

Hence, The ball to hit the ground in 0.53 s.

Final answer:

A baseball thrown horizontally with an initial speed will take the same amount of time to fall as a dropped object from the same height, which is 0.53 seconds, because the horizontal speed does not affect the vertical fall time.

Explanation:

The time it takes for an object to fall from a height solely depends on the force of gravity and the initial vertical speed. Since the baseball is thrown horizontally with an initial speed of 35 m/s, this speed does not affect the vertical fall time. The ball will hit the ground in the same duration as any object dropped from the same height without any initial vertical velocity, provided that air resistance is negligible. The previously stated object took 0.53 s to fall from a height of 1.4 m, therefore the baseball will also take 0.53 seconds to hit the ground.

Explanation:

It is given that,

Spring constant, k = 81 N/m

We need to find the force required to :

(a) Compress the spring by 6 cm i.e. x₁ = 6 cm = -0.06 m

It can be calculated using Hooke's law as :

F = - k(-x₁)

[tex]F=81\ N/m\times 0.06\ m[/tex]

F = 4.86 N

(b) Expand the spring by 17 cm i.e. x₂ = 17 cm = +0.17 m

So, F = -kx₂

[tex]F=-81\ N/m\times 0.17\ m[/tex]

F = -13.77 N

Hence, this is the required solution.

Final answer:

The force required to compress a spring with a spring constant of 81 N/m by 6 cm is 4.86 N, and the force required to expand the same spring by 17 cm is 13.77 N.

Explanation:

The force required to compress or expand a spring can be determined by Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the displacement (x) from its equilibrium position, and is given by the equation F = kx, where k is the spring constant.

To calculate the force required to:

Compress the spring by 6 cm:

First convert 6 cm to meters (6 cm = 0.06 m). Then apply Hooke's Law: F = kx = 81 N/m times 0.06 m = 4.86 N.

Expand the spring by 17 cm:

First convert 17 cm to meters (17 cm = 0.17 m). Then apply Hooke's Law: F = kx = 81 N/m times 0.17 m = 13.77 N.

In both cases, the magnitude of force is reported, as the question specifies, ignoring the sign which indicates the direction of the force.

Answer: v= 160ft/s

a=32ft/s^2 constant

Explanation:

s(t)=400-16t^2 derivative of position is velocity v(t) and derivative of velocity is acceleration a(t) so let s(t)=0 to find the time of flight to reach the ground and take the two derivatives and use the time found and solve. Also acceleration is a constant as it’s gravity.

0=400-16t^2

400=16t^2

25=t^2

t=5s

ds/dt=v(t)=0-32t

dv/dt=a(t)=-32 constant(gravity)

v(t)=-32(5s)= -160ft/s negative sign is only showing direction

The velocity of the object the moment it reaches the ground is 160 ft/s.

The problem can be solved by following steps.

s(t) = 400-16t^2 (given)

Let s(t)=0

Therefore

0= 400-16t^2

400=16t^2

25=t^2

Therefore

t = 5sec

Now as we know that the derivative of the position is Velocity

so v(t) = ds/dt = -32t

where t = 5sec

substitute the value of t in v(t)

Therefore, v(t) = -32(5) = -160

The direction is negative

Hence the velocity is 160ft/s

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