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American University in Cairo - PHYSICS 1011 PHYSICS HOMEWORK 41 ENERGY CONSERVATION WORK & ENERGY 1)A force of 25

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American University in Cairo - PHYSICS 1011

PHYSICS HOMEWORK 41 ENERGY CONSERVATION WORK & ENERGY

1)A force of 25.0 Newtons is applied so as to move a 5.0 kg mass a distance of 20.0 meters.

How much work was done?

2. A force of 120 N is applied to the front of a sled at an angle of 28.0? above the horizontal so as to pull the sled a distance of 165 meters. How much work was done by the applied force?
3. A sled, which has a mass of 45.0 kg., is sitting on a horizontal surface. A force of 120 N is applied to a rope attached to the front of the sled such that the angle between the front of the sled and the horizontal is 35.0º. As a result of the application of this force the sled is pulled a distance of 500 meters at a relatively constant speed. How much work was done to this sled by the applied force?

 

4. A rubber stopper, which has a mass of 38.0 grams, is being swung in a horizontal circle which has a radius of R = 1.35 meters. The rubber stopper is measured to complete 10 revolutions in 8.25 seconds.

   

1. 1. What is the speed of the rubber stopper?

?.?? ?

1. 2. How much force must be applied to the string in order to keep this stopper moving in this circular path at a constant speed?
   3. How far will the stopper move during a period of 25.0 seconds?

 

1. 4. How much work is done on the stopper by the force applied by the string during 25.0 seconds?

 

5. How much work would be required to lift a 12.0 kg mass up onto a table 1.15 meters high?

 

 

 

 

6. A barge is being pulled along a canal by two cables being pulled as shown to the right. The tension in each cable is T =14,000 N and each cable is being pulled at an angle ??= 18.0? relative to the direction of motion as shown. How much work will be done in pulling this barge a distance of 3.0 kilometers?

 

 

Kinetic Energy KE = ½ mv²

 

7. A car, which has a mass of 1250 kg is moving with a velocity of 26.0 m/sec.  What is the kinetic energy of this car?

 

8. What will be the kinetic energy of a bullet, which has a mass of 22.0 grams, moving with a velocity of 650 m/sec.?

 

9. How fast must a 4.40 kg bowling ball move in order to have a kinetic energy of 185 Joules? Ans. TKE = ½mv² ? 185 J = ½(4.40 kg)v² ? 185 = 2.20v² ? 84.09 = v² ? ?84.09 = ?v²     

 

10. A ball, which has a mass of 2.40 kg., is dropped from the top of a building 96.0 meters tall.
    1. How long will it take for this ball to reach the ground?
    2. What will be the velocity of the ball just as it reaches the ground?

 

1. 3. What will be the kinetic energy of the ball just as it reaches the ground?

 

1. 4. How much work would be needed to lift this ball back up to the top of the building at a constant speed?

 

 

 

11. A cart, which has a mass of m = 2.50 kg., is sitting at the top of an inclined plane which is 3.30 meters long and

which meets the horizontal at an angle of ??= 18.5?.       18.5?

1. 1. How long will it take for this cart to reach the bottom of the inclined plane?

 

 

1. 2. What will be the velocity of the cart when it reaches the bottom of the incline?

 

1. 3. What will be the kinetic energy of the cart when it reaches the bottom of the incline?

 

Gravitational Potential Energy GPE = mg?h

 

12. A 5.0 kg mass is initially sitting on the floor when it is lifted onto a table 1.15 meters high at a constant speed.
    1. How much work will be done in lifting this mass onto the table?

 

1. 2. What will be the gravitational potential energy of this mass, relative to the floor, once it is placed on the table?

 

1. 3. What was the initial gravitational potential energy, relative to the floor, of this mass while sitting on the floor?

 

13. A crate, which has a mass of 48.0 kg., is sitting at rest at the bottom of a frictionless inclined plane which is L = 2.85 meters long and

which meets the horizontal at an angle of ??= 31.5?^{. A force F is}             _31.5? applied so as to push the crate up this incline at a constant speed.

1. 1. What is the magnitude of the force F required to push the crate to the top of the incline at a constant speed?
2. How much work will be done in pushing the crate to the top of the incline?     

 

3. What is the height of this incline?         ? m

 

d. What will be the GPE of this crate when it reaches the top of the incline?

 

14. Suppose that you have a mass of 62.0 kg and that you walk to the top of a stairway which is F_y h = 12.0 meters high and L= 15.0 meters deep.
    1. How much work will you have to do in walking to the top of the stairway?
    2. What will be your GPE when you reach the top of the stairway?         15 m

 

Elastic Potential Energy EPE = ½ k(?x)² and [F = k?x]

15. A force of F = 35.0 N is applied to a spring and as a result the spring stretches a distance of

?x = 12.0 cm.

1. 1. What is the spring constant for this spring?

 

1. 2. How much energy will be stored in this spring?

 

16. A spring, which has a spring constant of k = 120 N/m, is being stretched a distance of         

?x = 15.0 cm by a force F.

1. 1. How much force F is being applied to this spring?

 

16. 2. How much energy will be stored in this spring?
17. A spring, which has a spring constant k, is hung from the ceiling as shown to the right. A mass m = 3.00 kg is added to the end of the spring and is then slowly lowered until equilibrium is reached. At this point the bottom of the mass has been lowered a distance of ?h = 52.0 cm.
    1. What is the magnitude of the force being exerted by the spring when the system reaches equilibrium?

 

1. 2. What is the spring constant of this spring?

 

1. 3. How much energy is stored in the spring when equilibrium is reached?

 

18. A mass of 5.00 kg is dropped from a height of 2.20 meters above a vertical spring sitting on a horizontal surface. Upon colliding with the spring the mass compresses the spring ?x = 30.0 cm before it momentarily comes to halt. [Assume h = 0 at the lowest point!]
    1. How much gravitational potential energy was contained in the 5.0 kg mass before it was dropped?

    

1. 2. How much energy will be stored in the spring when the mass comes briefly to a halt?
   3. What is the spring constant of this spring?

 

ENERGY CONSERVATION:

 

19. A cart, which has a mass of 2.30 kg is sitting at the top of           _{h =? m}

an inclined plane, which is 4.50 meters long and meets the         14?

horizontal at an angle of 14.0º. The car is then allowed to roll to the bottom of the incline;

1. 1. What was the gravitational energy of the cart before it rolls down the incline?
   2. What will be the magnitude of the force that tends to cause the cart to accelerate down the incline?

 

1. 3. What will be the acceleration of the cart as it moves down the incline?

 

 

1. 4. How much time to it take for the cart to reach the bottom of the incline?

 

1. 5. What will be the velocity of the cart as it reaches the bottom of the incline?

 

1. 6. What will be the kinetic energy of the cart as it reaches the bottom of the incline?

 

1. 7. How much work was done by the gravitational force on the cart as it rolls to the bottom of the incline?

 

20. A car is sitting at the top of an inclined plane, which is 5.2 meters long and meets the horizontal at an angle of 12.0º. The cart is then allowed to roll to the bottom of the incline. ^{h =? m}

What will be the velocity of the cart as it reaches the ^12? bottom of the incline?

 

 

 

    

 

21. A sled, which has a mass of 45.0 kg., is sitting on a ^Fy horizontal surface. A force of 120 N is applied to a rope _? = 35_?

attached to the front of the sled such that the angle between

the front of the sled and the horizontal is 35.0º. As a result ^Fx of the application of this force the sled is pulled a distance of 500 meters at a relatively constant speed. How much work was done to this sled by the applied force?

 

22. A 25.0 kg crate is sitting at the bottom of an inclined plane. The inclined plane is 12.0 meters long, meets the horizontal at an angle

of 15.0º and has a coefficient of sliding friction of ? = ^{0.55. A}                     _15.0?

force is applied to the crate so as to slide the crate up the incline at a constant speed.

1. 1. What will be the magnitude of the frictional force between the crate and the incline?

 

2. What will be the magnitude of the gravitational force component opposing the motion of the sled up the incline?

 

3. How much work will be done against the gravitational force in moving the crate to the top of the incline?

 

4. What is the magnitude of the force F required to push the sled up the incline at a constant speed?

 

 

 

5. How much work will be done by the applied force in pushing the mass to the top of the incline?

 

6. What will be the gravitational potential energy of the crate when it reaches the top of the incline?

   

7. How much work was done against the frictional force as the crate is pushed to the top of the incline?

 

8. How are the work done by the external force, the work done against friction and the work done against gravity related?

23. A box, which has a mass of 14.0 kg , is sliding along a horizontal surface with a velocity of 18.0 m/sec when it encounters a

frictionless inclined plane which meets the horizontal at an angle           28.0? of 28.0?. The box slides up the incline until it comes to a halt.

1. 1. 1. 1. What will be the kinetic energy of the crate before it reaches the bottom of the incline?

 

1. 1. 1. 2. What will be the gravitational potential energy of the crate when it finally stops on the incline? 

 

1. 1. 1. 3. How far up the incline will the box slide before it stops?