Question 1

A crane lifts a 425 kg steel beam vertically upward a distance of 117 m.How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

Accepted Answer

The work done by the crane is calculated using the formula: Work = Force × Distance. The force exerted by the crane is the sum of the gravitational force (mg) and the additional force due to acceleration (ma). Thus, Force = m(g + a) = 425 kg × (9.8 m/s² + 1.8 m/s²) = 425 kg × 11.6 m/s² = 4930 N. Therefore, Work = 4930 N × 117 m = 5.8 × 10⁵ J.

Question 2

The frame of a cart has a mass of 45 kg,and the cart rolls on four railroad car wheels,each with a mass of 22 kg.The cart is being ridden at a speed of 5.0 m/s by a 75 kg man.What is the total kinetic energy? (Model the railroad car wheels as solid uniform disks of radius 20 cm. )

Accepted Answer

The total kinetic energy is the sum of the kinetic energy of the frame, the kinetic energy of the wheels, and the kinetic energy of the man. The kinetic energy of the frame is (1/2)mv^2 = (1/2)(45 kg)(5.0 m/s)^2 = 562.5 J. The kinetic energy of each wheel is (1/2)Iω^2, where I is the moment of inertia of the wheel and ω is the angular velocity of the wheel. The moment of inertia of a solid uniform disk is (1/2)MR^2, where M is the mass of the disk and R is the radius of the disk. The angular velocity of the wheel is v/R, where v is the speed of the cart. Therefore, the kinetic energy of each wheel is (1/2)(1/2)MR^2(v/R)^2 = (1/4)Mv^2. The total kinetic energy of the wheels is 4(1/4)(22 kg)(5.0 m/s)^2 = 550 J. The kinetic energy of the man is (1/2)mv^2 = (1/2)(75 kg)(5.0 m/s)^2 = 937.5 J. Therefore, the total kinetic energy is 562.5 J + 550 J + 937.5 J = 2050 J.

Question 3

A massless spring hangs from the ceiling.How much does its potential energy increase,if a 28.8-kg mass is attached to it? The spring constant is 4800 N/m.

Accepted Answer

The potential energy of a spring is given by the equation PE = 1/2 kx^2, where k is the spring constant and x is the displacement from the equilibrium position. In this case, the displacement is equal to the weight of the mass, which is mg. So, the potential energy is:PE = 1/2 kx^2 = 1/2 k(mg)^2 = 1/2 (4800 N/m)(28.8 kg)^2 = 3724.8 J = 3.7 kJSo, the potential energy increases by 3.7 kJ.

Question 4

Calculate the kinetic energy of a 0.300 kg baseball thrown at a velocity of 44 m/s.

Accepted Answer

The kinetic energy (KE) is calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity. Substituting the given values: KE = 0.5 * 0.300 kg * (44 m/s)^2 = 290.4 J, which rounds to 290 J.

Question 5

An airplane is observed to be 2.68 km from its takeoff point,at a horizontal distance of 2.66 km.What is the gravitational potential energy of the plane with respect to the ground? The plane's mass is 23.0 metric tons.

Accepted Answer

The gravitational potential energy can be calculated using the formula: 
PE = mgh
where m is the mass of the plane, g is the acceleration due to gravity (9.8 m/s^2) and h is the height of the plane above the ground.

First, we need to find the height of the plane above the ground. We can use the Pythagorean theorem:

h = √(distance^2 - horizontal distance^2)
h = √(2.68^2 - 2.66^2)
h = 0.73 km

Now we can calculate the gravitational potential energy:

PE = (23.0 metric tons) * (1000 kg/metric ton) * (9.8 m/s^2) * (0.73 km)
PE = 166049.6 J = 166.05 MJ

Rounding to two significant figures, the answer is 73.7 MJ, which corresponds to choice (A).

Question 6

A block starts from rest at the top of a 31.0° inclined plane and encounters a spring,of constant 3.4 kN/m,rigidly attached to the plane.If the block's mass is 33.0 kg and it compresses the spring by 37.0 cm,find the distance the block travelled before it encountered the spring.

Accepted Answer

The correct answer is A because the block's initial potential energy is converted into kinetic energy and then into spring potential energy. The distance traveled before encountering the spring can be found using the conservation of energy:$$mgh = (1/2)mv^2 + (1/2)kx^2$$where m is the mass of the block, g is the acceleration due to gravity, h is the height of the inclined plane, v is the velocity of the block before encountering the spring, k is the spring constant, and x is the compression of the spring.Solving for h, we get:$$h = (v^2/2g) + (kx^2/2mg)$$Substituting the given values, we get:$$h = (0^2/2g) + (3.4 kN/m * (0.37 m)^2/2 * 33.0 kg * 9.81 m/s^2)$$$$h = 1.0 m$$

Question 7

4.00 × 10⁵ J of work are done on a 1110 kg car while it accelerates from 10.0 m/s to some final velocity.Find this final velocity.

Accepted Answer

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. The initial kinetic energy is (1/2) * 1110 kg * (10 m/s)^2. The final kinetic energy is (1/2) * 1110 kg * v^2. Setting the work done equal to the change in kinetic energy and solving for v gives approximately 28.6 m/s.

Question 8

Find the net work done by friction between the ground and the body of a snake slithering in a complete circle of 3.93 m radius.The coefficient of friction between the ground and the snake is 0.25,and the snake's weight is 54.0 N.

Accepted Answer

The net work done by friction is zero because the force of friction is always opposite to the direction of motion, and the displacement is zero over a complete circle.

Question 9

A child does 350 J of work while pulling a box from the ground up to his tree house with a rope.The tree house is 8.4 m above the ground.What is the mass of the box?

Accepted Answer

Work done = mgh350 = m * 9.8 * 8.4m = 4.3 kg

Question 10

You carry a 7.0 kg bag of groceries 1.2 m above the ground at constant velocity across a 2.3 m room.How much work do you do on the bag in the process?

Accepted Answer

When carrying an object at constant velocity horizontally, the work done against gravity is zero because there is no vertical displacement.

Question 11

A car drives 5.0 km north,then 7.3 km east,then 3.4 km northeast,all at a constant velocity.If the car had to perform 2.6 × 10⁶ J of work during this trip,what was the magnitude of the average frictional force on the car?

Accepted Answer

The work done by the frictional force is equal to the negative of the change in kinetic energy of the car. The change in kinetic energy is zero because the car starts and ends at rest. Therefore, the work done by the frictional force is equal to the negative of the total work done by the car. The total work done by the car is equal to the sum of the work done by the car in each leg of the trip. The work done by the car in each leg of the trip is equal to the product of the force applied to the car and the distance traveled by the car in that leg. The force applied to the car is equal to the magnitude of the average frictional force on the car. Therefore, the magnitude of the average frictional force on the car is equal to the negative of the total work done by the car divided by the total distance traveled by the car. The total work done by the car is equal to 2.6 × 10^6 J. The total distance traveled by the car is equal to 5.0 km + 7.3 km + 3.4 km = 15.7 km. Therefore, the magnitude of the average frictional force on the car is equal to 2.6 × 10^6 J / 15.7 km = 1.7 × 10^2 N.

Question 12

A spring stretches by 21.0 cm when a 135 N object is attached.What is the weight of a fish that would stretch the spring by 31.0 cm?

Accepted Answer

The spring constant k can be calculated using Hooke's Law: F = kx. For the 135 N object, k = 135 N / 0.21 m. For the fish, using the same k, the weight F = k * 0.31 m. Solving gives F = 199 N.

Question 13

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it bounce after the third time,provided we released it 2.3 m from the floor?

Accepted Answer

After the first bounce, the ball reaches a height of 2.3 * 0.78 = 1.794 m.
After the second bounce, the ball reaches a height of 1.794 * 0.78 = 1.399 m.
After the third bounce, the ball reaches a height of 1.399 * 0.78 = 1.09122 m or 109.122 cm, which can be rounded up to 110 cm.

Question 14

A helicopter descends vertically to land with a speed of 4.0 m/s.If the shock absorbers have an initial length of 0.50 m,they compress to 79% of their original length and the air in the tires absorbs 21% of the initial energy as heat,what is the ratio of the spring constant to the helicopter's mass? Assume one landing gear in the craft.

Accepted Answer

The energy absorbed by the shock absorbers is:$$E_s = \frac{1}{2}kx_0^2(1-0.79^2) = 0.36kx_0^2$$The energy absorbed by the air in the tires is:$$E_t = 0.21E_i = 0.21(mgh)$$The total energy absorbed is:$$E_a = E_s + E_t = 0.36kx_0^2 + 0.21mgh$$The work done by gravity is:$$W_g = mgh$$The ratio of the spring constant to the helicopter's mass is:$$\frac{k}{m} = \frac{E_a}{W_g} = \frac{0.36kx_0^2 + 0.21mgh}{mgh} = 0.36\frac{x_0^2}{h} + 0.21$$Substituting the given values, we get:$$\frac{k}{m} = 0.36\frac{(0.50 	ext{ m})^2}{4.0 	ext{ m}} + 0.21 = 1.1 	ext{ kN/kg-m}$$

Question 15

A traveler pulls on a suitcase strap at an angle 36° above the horizontal.If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m,what is the tension in the strap?

Accepted Answer

The answer of A traveler pulls on a suitcase strap...

Question 16

A horizontal spring-mass system oscillates on a frictionless table.If the ratio of the mass to the spring constant is 0.038 kg · m/N,and the maximum speed of the mass was measured to be 17.60 m/s,find the maximum extension of the spring.

Accepted Answer

The maximum extension of the spring is given by:$$x_{max} = \frac{mv_{max}^2}{k}$$where:* m is the mass of the object* v_{max} is the maximum speed of the object* k is the spring constantSubstituting the given values into the equation, we get:$$x_{max} = \frac{(0.038 	ext{ kg})(17.60 	ext{ m/s})^2}{k}$$$$x_{max} = 3.4 	ext{ m}$$Therefore, the correct answer is A.

Question 17

A 1000.0 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s.How far does it travel while slowing down?

Accepted Answer

Using the work-energy principle, the work done by the net force equals the change in kinetic energy. The initial kinetic energy is (1/2)*1000*(30)^2 and the final kinetic energy is (1/2)*1000*(23.4)^2. The work done is force times distance, so 9500*d = change in kinetic energy. Solving for d gives approximately 19 m.

Question 18

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long,until the swing makes an angle of 32.0° with the vertical.What is your sister's mass?

Accepted Answer

The work done is equal to the change in potential energy of the system. The change in potential energy is equal to the mass of the system times the acceleration due to gravity times the change in height. The change in height is equal to the length of the chain times the sine of the angle. So, the mass of the system is equal to the work done divided by the acceleration due to gravity times the length of the chain times the sine of the angle. Plugging in the given values, we get:$$m = \frac{W}{gL\sin	heta} = \frac{174 J}{(9.8 m/s^2)(5.10 m)\sin32.0^\circ} = 22.9 kg$$

Question 19

A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below.If the balloon is traveling at 30.3 m/s when it strikes a person's head (1.5 m above the ground),how tall is the building? Neglect air resistance.

Accepted Answer

Using the kinematic equation $ v^2 = u^2 + 2as $, where $ v = 30.3 \, \text{m/s} $, $ u = 0 \, \text{m/s} $, $ a = 9.8 \, \text{m/s}^2 $, and $ s $ is the distance fallen. Solving for $ s $, we get $ s = \frac{v^2}{2a} = \frac{(30.3)^2}{2 \times 9.8} \approx 46.8 \, \text{m} $. Adding the 1.5 m height of the person, the building is approximately 48 m tall.

Question 20

A block slides down a frictionless inclined ramp.If the ramp angle is 17.0° and the length of it is 30.0 m,find the speed of the block as it reaches the end of the ramp,assuming it started sliding from rest at the top.

Accepted Answer

The speed can be found using energy conservation: potential energy at the top equals kinetic energy at the bottom. The height (h) is 30.0 m * sin(17.0°). Using the formula v = sqrt(2gh), where g = 9.8 m/s², the speed is approximately 13.1 m/s.

Quiz 10: Energy and Work

A crane lifts a 425 kg steel beam vertically upward a distance of 117 m.How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

The frame of a cart has a mass of 45 kg,and the cart rolls on four railroad car wheels,each with a mass of 22 kg.The cart is being ridden at a speed of 5.0 m/s by a 75 kg man.What is the total kinetic energy? (Model the railroad car wheels as solid uniform disks of radius 20 cm. )

A massless spring hangs from the ceiling.How much does its potential energy increase,if a 28.8-kg mass is attached to it? The spring constant is 4800 N/m.

Calculate the kinetic energy of a 0.300 kg baseball thrown at a velocity of 44 m/s.

An airplane is observed to be 2.68 km from its takeoff point,at a horizontal distance of 2.66 km.What is the gravitational potential energy of the plane with respect to the ground? The plane's mass is 23.0 metric tons.

A block starts from rest at the top of a 31.0° inclined plane and encounters a spring,of constant 3.4 kN/m,rigidly attached to the plane.If the block's mass is 33.0 kg and it compresses the spring by 37.0 cm,find the distance the block travelled before it encountered the spring.

4.00 × 10⁵ J of work are done on a 1110 kg car while it accelerates from 10.0 m/s to some final velocity.Find this final velocity.

Find the net work done by friction between the ground and the body of a snake slithering in a complete circle of 3.93 m radius.The coefficient of friction between the ground and the snake is 0.25,and the snake's weight is 54.0 N.

A child does 350 J of work while pulling a box from the ground up to his tree house with a rope.The tree house is 8.4 m above the ground.What is the mass of the box?

You carry a 7.0 kg bag of groceries 1.2 m above the ground at constant velocity across a 2.3 m room.How much work do you do on the bag in the process?

A car drives 5.0 km north,then 7.3 km east,then 3.4 km northeast,all at a constant velocity.If the car had to perform 2.6 × 10⁶ J of work during this trip,what was the magnitude of the average frictional force on the car?

A spring stretches by 21.0 cm when a 135 N object is attached.What is the weight of a fish that would stretch the spring by 31.0 cm?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it bounce after the third time,provided we released it 2.3 m from the floor?

A traveler pulls on a suitcase strap at an angle 36° above the horizontal.If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m,what is the tension in the strap?

A horizontal spring-mass system oscillates on a frictionless table.If the ratio of the mass to the spring constant is 0.038 kg · m/N,and the maximum speed of the mass was measured to be 17.60 m/s,find the maximum extension of the spring.

A 1000.0 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s.How far does it travel while slowing down?

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long,until the swing makes an angle of 32.0° with the vertical.What is your sister's mass?

A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below.If the balloon is traveling at 30.3 m/s when it strikes a person's head (1.5 m above the ground) ,how tall is the building? Neglect air resistance.

A block slides down a frictionless inclined ramp.If the ramp angle is 17.0° and the length of it is 30.0 m,find the speed of the block as it reaches the end of the ramp,assuming it started sliding from rest at the top.

Quiz 10: Energy and Work

A crane lifts a 425 kg steel beam vertically upward a distance of 117 m.How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces.

The frame of a cart has a mass of 45 kg,and the cart rolls on four railroad car wheels,each with a mass of 22 kg.The cart is being ridden at a speed of 5.0 m/s by a 75 kg man.What is the total kinetic energy? (Model the railroad car wheels as solid uniform disks of radius 20 cm. )

A massless spring hangs from the ceiling.How much does its potential energy increase,if a 28.8-kg mass is attached to it? The spring constant is 4800 N/m.

Calculate the kinetic energy of a 0.300 kg baseball thrown at a velocity of 44 m/s.

An airplane is observed to be 2.68 km from its takeoff point,at a horizontal distance of 2.66 km.What is the gravitational potential energy of the plane with respect to the ground? The plane's mass is 23.0 metric tons.

A block starts from rest at the top of a 31.0° inclined plane and encounters a spring,of constant 3.4 kN/m,rigidly attached to the plane.If the block's mass is 33.0 kg and it compresses the spring by 37.0 cm,find the distance the block travelled before it encountered the spring.

4.00 × 105 J of work are done on a 1110 kg car while it accelerates from 10.0 m/s to some final velocity.Find this final velocity.

Find the net work done by friction between the ground and the body of a snake slithering in a complete circle of 3.93 m radius.The coefficient of friction between the ground and the snake is 0.25,and the snake's weight is 54.0 N.

A child does 350 J of work while pulling a box from the ground up to his tree house with a rope.The tree house is 8.4 m above the ground.What is the mass of the box?

You carry a 7.0 kg bag of groceries 1.2 m above the ground at constant velocity across a 2.3 m room.How much work do you do on the bag in the process?

A car drives 5.0 km north,then 7.3 km east,then 3.4 km northeast,all at a constant velocity.If the car had to perform 2.6 × 106 J of work during this trip,what was the magnitude of the average frictional force on the car?

A spring stretches by 21.0 cm when a 135 N object is attached.What is the weight of a fish that would stretch the spring by 31.0 cm?

A tennis ball bounces on the floor three times.If each time it loses 22.0% of its energy due to heating,how high does it bounce after the third time,provided we released it 2.3 m from the floor?

A traveler pulls on a suitcase strap at an angle 36° above the horizontal.If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m,what is the tension in the strap?

A horizontal spring-mass system oscillates on a frictionless table.If the ratio of the mass to the spring constant is 0.038 kg · m/N,and the maximum speed of the mass was measured to be 17.60 m/s,find the maximum extension of the spring.

A 1000.0 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s.How far does it travel while slowing down?

You do 174 J of work while pulling your sister back on a swing,whose chain is 5.10 m long,until the swing makes an angle of 32.0° with the vertical.What is your sister's mass?

A prankster drops a water balloon from the top of a building on an unsuspecting person on the sidewalk below.If the balloon is traveling at 30.3 m/s when it strikes a person's head (1.5 m above the ground) ,how tall is the building? Neglect air resistance.

A block slides down a frictionless inclined ramp.If the ramp angle is 17.0° and the length of it is 30.0 m,find the speed of the block as it reaches the end of the ramp,assuming it started sliding from rest at the top.

A crane lifts a 425 kg steel beam vertically upward a distance of 117 m.How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

4.00 × 10⁵ J of work are done on a 1110 kg car while it accelerates from 10.0 m/s to some final velocity.Find this final velocity.

A car drives 5.0 km north,then 7.3 km east,then 3.4 km northeast,all at a constant velocity.If the car had to perform 2.6 × 10⁶ J of work during this trip,what was the magnitude of the average frictional force on the car?