Physics Homework
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Momentum

1.

A 30 cm spring with constant 70 N/m is compressed to 10 cm and placed between two carts. Cart A has mass = 5kg and is unknown. Initially the system is at rest. After it is released it is observed that cart A has three times the velocity of cart B.
a) What force must be exerted initially to keep the spring compressed?

b) What is the work done to compress the spring?

c)

By considering conservation of momentum determine the mass
d) By considering conservation of energy find the velocities of the carts A and B after the spring is released.

2. A 0.30 kg ball is dropped onto a concrete driveway. The ball’s velocity before impact is 4.5 m/s and after impact is 4.2 m/s. What is the change in the ball’s momentum?

3. A 1.5 kg ball falls onto a floor. Just before it strikes the floor, its velocity is 12 m/s. The ball bounces up with a velocity of 10 m/s. Find the impulse on the ball.

4. A soccer player kicks a soccer ball initially at rest setting it in motion at a velocity of 30 m/s. If the ball has a mass of 0.50 kg and the time of contact is 0.025 s, what is the force exerted on the player’s foot?

5. A 1000 kg car traveling east at 20 m/s collides head-on with a 1500 kg car traveling west at 10 m/s. The cars stick together after the collision. What is their common velocity after the collision?

6. A 0.240 kg glider moving with a velocity of 0.600 m/s collides head-on with a 0.260 kg glider moving along the same line in the opposite direction with a velocity of 0.200 m/s. The collision is perfectly inelastic. What is the final velocity of the combined gliders?

7. A 15,000 kg railroad freight car is coasting at a speed of 2.0 m/s. It collides and couples with another car with a mass of 50,000 kg, which was initially not moving. What percentage of the initial kinetic energy of the system is preserved after collision?

8. A ballistic pendulum is a device used to measure the speed of a bullet. A bullet is fired at a block of wood hanging from two strings. The bullet embeds itself in the block and causes the combined block plus bullet system to swing up. If the bullet is fired at 530 m/s and its mass is 6.5 g, what is the speed of the block and the embedded bullet after collision? The mass of the block is 2.2 kg.

9. Using the same data from question 8, and the answer to question 8, how high will the pendulum’s block and the embedded bullet rise?

10. A bumper protects a car during a collision because it:

a) increases the time of impact

b) decreases the time of impact

c) increases the force of impact

d) increases kinetic energy transfer

Rotation

1. A Ferris wheel with a radius of 27.5 m makes one complete revolution in 25.0 s.

a) What is the linear speed of a rider on the wheel?

b) What is the magnitude of the centripetal acceleration of a rider?

2. A 1.5 kg ball on a 0.9 m long string is spun in a circle with a velocity of 8 m/s. What is its centripetal force and centripetal acceleration?

3. A wrench is used to loosen a bolt. If a torque of 55 Nm is required to loosen the bolt and the person is only capable of exerting a maximum of 70 N, what is the minimum lever arm needed to loosen the bolt?

4. If an ice skater spins three times each second with her arms straight out and tucks them in to cut her rotational inertia in half, how many rotations per second will result? Support your answer.

5. A passenger on a Ferris wheel moves in a vertical circle of radius R=8.0m with constant speed v. If the wheel makes one revolution in 10.0s, what is the linear speed v? What is the angular speed ??

6. A small car with mass m and a large car with mass 2m drive around a highway curve of radius R with the same speed v. As they travel around the curve, their accelerations are (explain the answer with detailed explanation or calculations!): (a) equal (b) along the direction of motion (c) in the ratio of 2 to 1 (d) zero

7. Nancy has a mass of 60 kg and sits on the very end of a 3.00 m long plank pivoted in the middle. How much torque must her co-worker provide on the other end of the plank in order to keep Nancy from falling on the ground?

8. What is the linear velocity of the center of a circle of radius 1 m rotating with angular velocity 2 rad/s?

9. An object moving in a circle of radius 2 m accelerates at a rate of 10 m/s2. What is the angular acceleration of the object?

10. An object travels a distance of 2 m, making a complete revolution around a circle. What is the radius of the circle?

Newton’s Law of Universal Gravitation

1) Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and the other has a mass of 52.0 kg. What is the gravitational force between them?

2) What gravitational force does the moon produce on the Earth is their centers are 3.88×108 m apart and the moon has a mass of 7.34×1022 kg?

3) If the gravitational force between objects of equal mass is 2.30×10?8 N when the objects are 10.0 m apart, what is the mass of each object?

4) Calculate the gravitational force on a 6.50×102 kg that is 4.15×106 m above the surface of the Earth?

5) The gravitational force between two objects that are 2.1×10?1 m apart is 3.2×10?6 N. If the mass of one object is 55 kg what is the mass of the other object?

6) If two objects, each with a mass of 2.0×102 kg, produce a gravitational force between them of 3.7×10?6 N. What is the distance between them?

7) What is the gravitational force acting on a 70.0 kg object standing on the Earth’s surface?

8) What is the gravitational force on a 35.0 kg object standing on the Earth’s surface? (You can use your answer from #7 to reduce your calculations)

9) What is the gravitational force on a 70.0 kg that is 6.38×106 m above the Earth’s surface? (You can use your answer from #7 to reduce your calculations)

10) Three objects each with a mass of 10.0 kg are placed in a straight line 50.0 cm apart. What is the net gravitational force on the center object due to the other two?

11) Three objects A, B, C are placed 50.0 cm apart along a straight line. A and B have a mass of 10.0 kg, while C has a mass of 15.0 kg. What is the net force on B due to A and C?

(Thermodynamics) Specific Heat

Use q = (m)(?T)(Cp) to solve the following problems. Show all work and units.

1. A 15.75-g piece of iron absorbs 1086.75 joules of heat energy, and its temperature changes from 25°C to 175°C. Calculate the specific heat capacity of iron.

1. How many joules of heat are needed to raise the temperature of 10.0 g of aluminum from 22°C to 55°C, if the specific heat of aluminum is 0.90 J/g°C?

1. To what temperature will a 50.0 g piece of glass raise if it absorbs 5275 joules of heat and its specific heat capacity is 0.50 J/g°C? The initial temperature of the glass is 20.0°C.

1. Calculate the heat capacity of a piece of wood if 1500.0 g of the wood absorbs 6.75×104 joules of heat, and its temperature changes from 32°C to 57°C.

1. 100.0 mL of 4.0°C water is heated until its temperature is 37°C. If the specific heat of water is 4.18 J/g°C, calculate the amount of heat energy needed to cause this rise in temperature.

1. 25.0 g of mercury is heated from 25°C to 155°C, and absorbs 455 joules of heat in the process. Calculate the specific heat capacity of mercury.

1. What is the specific heat capacity of silver metal if 55.00 g of the metal absorbs 47.3 calories of heat and the temperature rises 15.0°C?

1. If a sample of chloroform is initially at 25°C, what is its final temperature if 150.0 g of chloroform absorbs 1.0 kilojoules of heat, and the specific heat of chloroform is 0.96 J/g°C?

1. How much energy must be absorbed by 20.0 g of water to increase its temperature from 283.0 °C to 303.0 °C? (Cp of H2O = 4.184 J/g °C)

10. When 15.0 g of steam drops in temperature from 275.0 °C to 250.0 °C, how much heat energy is released?

(Cp of H2O = 4.184 J/g °C)

11. How much energy is required to heat 120.0 g of water from 2.0 °C to 24.0 °C? (Cp of H2O = 4.184 J/g °C)

12. How much heat (in J) is given out when 85.0 g of lead cools from 200.0 °C to 10.0 °C? (Cp of Pb = 0.129 J/g °C)

13. If it takes 41.72 joules to heat a piece of gold weighing 18.69 g from 10.0 °C to 27.0 °C, what is the specific heat

of the gold?

14. A certain mass of water was heated with 41,840 Joules, raising its temperature from 22.0 °C to 28.5 °C. Find the

mass of the water, in grams. (Cp of H2O = 4.184 J/g °C)

15. How many joules of heat are needed to change 50.0 grams of ice at -15.0 °C to steam at 120.0 °C?

(Cp of H2O = 4.184 J/g °C)

16. Calculate the number of joules given off when 32.0 grams of steam cools from 110.0 °C to ice at -40.0 °C.

(Cp of H2O = 4.184 J/g °C)

17. The specific heat of ethanol is 2.46 J/g oC. Find the heat required to raise the temperature of 193 g of ethanol

from 19oC to 35oC.

18. When a 120 g sample of aluminum (Al) absorbs 9612 J of energy, its temperature increases from 25oC to 115oC.

Find the specific heat of aluminum.

Fluids

1. A hydraulic lift is used to lift heavy machine pushing down on a 5 square meters piston with a force of 1000 N. What force needs to be applied on the 1 square meter piston to lift the machine.

1. A water tower has a vertical pipe that is filled with water. The pipe is open to the atmosphere at the top. The pipe is 22 m high. What is the pressure at the bottom?

1. The Mariana trench is in the Pacific Ocean and has a depth of approximately 11,000 m. The density of seawater is approximately 1025 kg/m3. What force would someone experience at such depth?

1. How deep do you need to go under water to double the atmospheric pressure of 1 atm? Water density is exactly 1000 kg/m3.

1. A tennis ball has a density of 0.084 g/cm3 and a diameter of 3.8 cm. What force is required to submerge the ball in water?

1. Eddie is driving his car and gets a flat tire. He pulls out his hydraulic jack to lift his car. If he exerts a force of 83 N on the handle of the jack and the diameter of the input piston is 125 mm, then what must the diameter of the output piston be if his car is 1100 kg?

A

m

B

m