Question 1

You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under identical conditions?

Accepted Answer

The answer of You slam on the brakes of your...

Question 2

In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

Accepted Answer

The answer of In the figure, two boxes, each of...

Question 3

A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min, what is the average power generated by the child?

Accepted Answer

Power is calculated as work done over time. Work done is force times distance (75 N * 42 m = 3150 J). Time is 3.0 min, which is 180 seconds. Power = 3150 J / 180 s = 17.5 W, which rounds to 18 W.

Question 4

A 4.00-kg mass is attached to a very light ideal spring hanging vertically and hangs at rest in the equilibrium position. The spring constant of the spring is 1.00 N/cm. The mass is pulled downward 2.00 cm and released. What is the speed of the mass when it is 1.00 cm above the point from which it was released?

Accepted Answer

First, we need to find the potential energy of the spring-mass system when it is pulled downward. The formula for potential energy stored in a spring is given by:

$$U = \frac{1}{2}kx^2$$

where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. We know that the mass is pulled 2 cm downward, so $x = 2$ cm = 0.02 m. Substituting the values, we get:

$$U = \frac{1}{2}(1.00 N/cm)(0.02 m)^2 = 0.0002 J$$

This potential energy is converted to kinetic energy as the mass moves upward. At any point during this motion, the total energy (potential + kinetic) of the system must be constant. So we can write:

$$U_i + K_i = U_f + K_f$$

where the subscripts $i$ and $f$ denote the initial and final states, respectively. We are interested in finding the final kinetic energy, so we can rearrange the equation as:

$$K_f = U_i + K_i - U_f$$

We know that $U_i = 0$, since the mass starts from the equilibrium position. We also know that at the highest point (when the mass is 1 cm above the equilibrium position), the spring is compressed by 1 cm, so $x = -0.01$ m. The potential energy at this point is:

$$U_f = \frac{1}{2}(1.00 N/cm)(-0.01 m)^2 = 0.0000005 J$$

So we have:

$$K_f = 0 + U_i - U_f = 0.0002 J - 0.0000005 J = 0.0001995 J$$

At any point during the motion, the speed of the mass is given by:

$$v = \sqrt{\frac{2K}{m}}$$

where $K$ is the kinetic energy, and $m$ is the mass. Substituting the values, we get:

$$v = \sqrt{\frac{2(0.0001995 J)}{4.00 kg}} \approx 0.0866 m/s$$

So the correct answer is (D).

Question 5

A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m²)x² If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

Accepted Answer

The answer of A 7.0-kg rock is subject to a...

Question 6

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?

Accepted Answer

Instantaneous power is the derivative of work with respect to time, so:P = dW/dt = 3at^2At t = 3.7 s, the instantaneous power is:P = 3(2.4 J/s^3)(3.7 s)^2 = 99 W

Question 7

If electricity costs 6.00¢/kWh (kilowatt-hour), how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

Accepted Answer

First, convert the power of the stereo system to kilowatts: 120 W = 0.12 kW. Then, calculate the total energy used in 4 weeks (28 days): 0.12 kW * 4 hours/day * 28 days = 13.44 kWh. Finally, calculate the cost: 13.44 kWh * 6.00¢/kWh = 80.64¢, which rounds to $0.81.

Question 8

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

Accepted Answer

The power output of the motor is:$$P = 7.08 	ext{ hp} \left( \frac{746 	ext{ W}}{1 	ext{ hp}} ight) = 5280 	ext{ W}$$The work done in lifting the beam is:$$W = Fd = mgh = (250 	ext{ kg})(9.8 	ext{ m/s}^2)(45.0 	ext{ m}) = 1.10 	imes 10^5 	ext{ J}$$The time it takes to do the work is:$$t = \frac{W}{P} = \frac{1.10 	imes 10^5 	ext{ J}}{5280 	ext{ W}} = 20.9 	ext{ s}$$

Question 9

A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.)? (1 hp = 746 W)

Accepted Answer

The power needed to overcome the resistive force is equal to the power generated by the car. Therefore, the magnitude of the total resistive force is:$$P = Fv$$$$F = \frac{P}{v} = \frac{75.0 	ext{ hp} 	imes 746 	ext{ W/hp}}{27.3 	ext{ m/s}} = 2.05 	imes 10^3 	ext{ N}$$

Question 10

The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at x = 2.00 m, what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

Accepted Answer

The answer of The force on a 3.00-kg object as...

Question 11

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp = 746 W)

Accepted Answer

The answer of A 1500-kg car accelerates from 0 to...

Question 12

An unusual spring has a restoring force of magnitude F = (2.00 N/m)x + (1.00 N/m²)x², where x is the stretch of the spring from its equilibrium length. A 3.00-kg object is attached to this spring and released from rest after stretching the spring 1.50 m. If the object slides over a frictionless horizontal surface, how fast is it moving when the spring returns to its equilibrium length?

Accepted Answer

The answer of An unusual spring has a restoring force...

Question 13

A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

Accepted Answer

Using the formula for kinetic energy, we have:

$K_i = K_f + W_{fr}$

$\frac{1}{2}mv_i^2 = \frac{1}{2}mv_f^2 + W_{fr}$

$W_{fr} = \frac{1}{2}mv_i^2 - \frac{1}{2}mv_f^2$

$W_{fr} = \frac{1}{2}m(v_i^2 - v_f^2)$

$W_{fr} = \frac{1}{2}m[(3.00 	ext{ m/s})^2 - 0^2]$

$W_{fr} = \frac{9}{2}m$

The work done by friction is equal to the force of friction multiplied by the distance. Using Newton's laws, we know that the force of friction is equal to the normal force times the coefficient of friction. Therefore:

$W_{fr} = f_f d = \mu_k N d$

$\frac{9}{2}m = \mu_k mgd$

$\mu_k = \frac{9}{2gd} = \frac{9}{2 \cdot 9.81 \cdot 4.00} \approx 0.115$

So the coefficient of kinetic friction is approximately 0.115, which is choice C.

Question 14

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

Accepted Answer

The minimum average power output is calculated using the formula P = (mgh)/t, where m is mass, g is acceleration due to gravity, h is the vertical height, and t is time. First, calculate the vertical height: h = 12.0 m * sin(25.0°). Then, substitute m = 55.8 kg, g = 9.81 m/s², and t = 3.00 s into the formula. Convert the result from watts to horsepower by dividing by 746 W/hp. The calculation gives approximately 1.24 hp.

Quiz 6: Work and Kinetic Energy

You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under identical conditions?

In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min, what is the average power generated by the child?

A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m²)x² If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?

If electricity costs 6.00¢/kWh (kilowatt-hour) , how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.) ? (1 hp = 746 W)

The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at x = 2.00 m, what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp = 746 W)

A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

Quiz 6: Work and Kinetic Energy

You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under identical conditions?

In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min, what is the average power generated by the child?

A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m2)x2 If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

The work performed as a function of time for a process is given by W = at3 where a = 2.4 J/s3. What is the instantaneous power output at t = 3.7 s?

If electricity costs 6.00¢/kWh (kilowatt-hour) , how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.) ? (1 hp = 746 W)

The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at x = 2.00 m, what will its speed be when it reaches x = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp = 746 W)

A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

A 7.0-kg rock is subject to a variable force given by the equation F(x) = 6.0 N - (2.0 N/m)x + (6.0 N/m²)x² If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

The work performed as a function of time for a process is given by W = at³ where a = 2.4 J/s³. What is the instantaneous power output at t = 3.7 s?