1.  a.  State the work- Energy theorem in equation form.

b.  State the law of conservation of energy.

c.  State Newton's second law in equation form.

d.  What  must always be the positive direction in a circular motion problem and why?

e.  State the Impulse - Momentum Theorem in equation form.

 

2.  A girl stands on a bathroom scale inside an elevator.  When the elevator is at rest, the scale reads

750 N (170 lb).  State whether the scales reading increases, decreases, or remains the same when:

 

a.  The elevator is moving upward at an increasing speed.

b.  The elevator is moving upward at a decreasing speed.

c.  The elevator is moving upward at constant speed.

d.  The elevator is moving downward at decreasing speed.

e.  The elevator is moving downward at constant speed.

f.  On a freebody diagram, the name we give the scales reading is the ________________ force because the direction of this force is always perpendicular to the plane of contact.

 

3.

 

4. 


5.   A 20 kg mass is pulled along on a horizontal plane by a horizontal force of 50 N.  The coefficient of kinetic  friction between the plane and the mass is 0.2 .  What is the acceleration of the mass?

 

6.   An object slides down a  plane whose incline makes an angle of 53¡ with the horizontal.  It's acceleration down the plane is 4 m/s2.  What is the coefficient of kinetic friction ?

 

7.  A 30 kg  object is pushed along a horizontal surface at constant speed  by the force indicated.  The coefficient of kinetic friction between surfaces is 0.3 .  What is the magnitude of the force F ?

 

8.   A 20 kg mass is pulled along on a friction free horizontal plane by a horizontal force of 50 N.   What is the acceleration of the mass?

 

9.   An object slides down a  friction free plane with an acceleration of 4 m/s2.  What angle does the plane make with the horizontal ?

 

10.

 

11.  Two objects are attached to a massless, friction free pully as indicated in the figure.   Draw a FBD for the 3 kg object.

 

12.  The surfaces are friction free.   The 3 kg block acclerates 5 m/s2 to the right.  Find the magnitude of F.

 

13.  The pulley is massless and friction free, the surface has  friction.  Draw a FBD for the 9 kg box.

14. The mechanic is raising this 300-pound engine at a constant rate using the frictionless pulley system shown. With how much force is he pulling on the rope?

 

1 . 600 lbs           

 

2.  450 lbs.

 

3. 300 lbs.     

 

4. 200 lbs.

 

5. 150 lbs.

 

6. 100 lbs.

 

7. 50 lbs.

 

8 . impossible to determine

15.  Determine the reading of each of the scales in the figure below.  (hint:  draw a FBD and sum the forces for each pulley and the 100 N block.)

 

16.  Determine the reading of each of the scales in the figure below.  (hint:  draw a FBD and sum the forces for each pulley and the block.)

 

17.  A 100 kg slab is supported by three ropes and two 50 kg pulleys.  The system is stationary.

Find T.

 

 

18. 

 

19.  Two blocks connected by a massless rope are being dragged by a force of 60 N, as indicated in the figure below.

If m1 = 4 kg and m2 = 8 kg, and µk = 0.3  , find

 

 

a.  Find the acceleration of the system.

 

 

b.  Find the tension T in the rope.

 

20.    Elvira pushes on the box with all her might horizontally.  The block acclerates up the hill 2 m/s2.  If the coefficient of kinetic friction between the box and the hill is µk = .4, what is the force F with which Elvira pushes the box?

 

 

 21.  A 5 kg penguin sits on a 12 kg sled as shown in the figure below.  A horizontal force of 45 N is applied to the sled, but the penguin attempts to impede the motion of the sled by holding onto a rope attached to the wall.  The coefficient of kinetic friction betwen the sled and the snow, as well as between the penguin's feet and the sled is 0.2.

 

a.  Draw a FBD for the penguin.

 

b.  List all the forces acting on the penguin

 

c.  List the reaction force for each force acting on the penguin.

 

Find the tension in the rope

 

Find the acceleration of the sled.

 

22.  A 5-kg penguin sits on top of a 10-kg sled, as in Figure below.  A force of 45 N is applied to the sled down the plane as indicated, but the penguin attempts to impede the motion by holding onto a cord attached to a wall The coefficient of kinetic friction between the moving surfaces is 0.2.

 

Draw the force diagram for the penguin and identify the Newton's third law reaction force for each force you include.

 

   

 

 

23.  The cart full of goodies speeds toward the cabin at increasing speed.  As the miner enters the antigravity cloud below, tension T in the rope suddenly drops in half.   What happens to the carts velocity at this point?  (You must draw a FBD to receive any credit.)  You must explain  your answer.

 

 

 

24.  A 1000 kg car goes over a hill and is located as indicated on the figure below.

 

a.  Find the normal force of the hill on the car at this point if it is at rest.

 

 

b. Find the normal force if the car is moving at 40 mph.

 

 

25.    A 30-kg child rides on a circus Ferris wheel that takes her around a vertical circular path with a radius of 20 m every 22 s.  What is the magnitude of the resultant force on the child at the highest point on this trajectory?

(You must draw a FBD to receive any credit.)

                       a.         49 N

                       b.         0.29 kN

                       c.         0.34 kN

                       d.         0.25 kN

                       e.         0.76 kN

 

26.    A 400 N kid rides a Ferris Wheel at the circus.  She is sitting on a scales, to see how her weight (accrding to the scales ) varies as she goes around.  The Ferris Wheel has a radius of 40 m and she is moving with a constant speed .  If the strap holding her in the seat must exert a force of 100 N down to hold her in the seat at the top of the ride,

a)  How fast is she moving?  (You must draw a FBD to receive any credit.)

 

b) What does the scales read at the bottom of the of the Ferris Wheel?  (You must draw a FBD to receive any credit.)

 

 

27.  A space station of diameter 80 m is turning about its axis at a constant rate.  If the acceleration of the outer rim of the station is 2.5 m/s2, what is the period of revolution of the space station?

      

                       a.         22 s

                       b.         19 s

                       c.         25 s

                       d.         28 s

                       e.         40 s

 

28.   A 20 kg mass is rotated in a circle  by means of a string attached to it and the center of a circle of radius 4 m on a horizontal friction free surface with a speed of 6 m/s.  What is the tension in the string ?

 

29.   An automobile rounds a curve of radius 50 m on a flat highway at 100 m/s.   What is the coefficient of static friction  between the roadway and the tires?

 

A 3 kg ball is rotated in a vertical circle at the end of a string with a constant 6 revolutions per minute. 

 

Find the tension in the string at the top of the circle.

 

Find the tension in the string at the bottom of the circle.

 

30.   A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point (6i – 8j) m.  How much  work is done by the given force during this displacement?

 

                       a.         +60 J

                       b.         +84 J

                       c.         +72 J

                       d.         +48 J

                       e.         +57 J

 

 

31. If a force F = (3i - 5j)N acts on a box of goodies over a displacement of  r = ( 2i - 5j) m, find the work done on the box by the force.

 

32.   Given that F = 3i - 4 j and Dr = -2i + j , find the work done by the force F over the displacement Dr.

 

b.  How much work is done on a Hooke's Law spring with a spring constant of 45 N/m when stretching it 3 m from it's equilibrium position?

 

c.  If it takes 8 J to stretch a Hooke's law spring 20 cm from it's equilibrium position, how much work is required to stretch it an additional 20 cm ?

 

d.  How much work is required to increase the speed of a 400 kg object from 30 m/s to 50 m/s?

 

33.   How much work is done by the force F in the F vs x curve below.

 

 

34.  Find the speed with which the 2 kg block strikes the floor.   The objects start from rest and the coefficient of friction between the 3 kg block and the table is 0.3.  (Assume the pulley and string are massless.)

 

 

 

35.    What is the velocity of the 50 kg block sliding down the loop - the - loop ramp at B if the track is friction free.

 

 

 

36.   A block slides down a plane and compresses a spring when coming to rest.  If the coefficient of kinetic friction between the block and the plane is µk = .3 and the spring is compressed 2 m, what is the spring stiffness constant of the spring?

 

 

 

 

37.  A block sliding with a velocity of 20 m/s slides up a friction free plane and collides with a spring whose spring stiffness constant is 500 N/m.  If the incline is as indicated in the diagram below, how far does the spring get depressed?

 

 

 

In a land not very far away, a popular sport is to do the yellow jello slam on a skate board.  A 60 kg skate boarder is zooming along at 28 m/s when she slams into the giant blob of jello.  She exits the other side  4 seconds later drenched in yucky jello travelling only 12 m/s. 

 

38.    How much work is done on the drenched damsel by the yellow blob?

 

39.   What is the average force the blob imposes on the skate boarder?

 

 

Karol is skating along and throws the 30 kg ball to Karl (also on skates), who is standing still,  with a velocity of 25 m/s relative to the earth.  The impulse of this effort slows her to a speed of 20 m/s.

 

 

41.  What was Karol's velocity before she threw the ball ?

 

 

42.  What will Karl's speed be after he catches the ball?

 

43. A 60 kg kid on a 200 kg bumper car is moving to the east at 80 m/s.  She has a head-on perfectly inelastic collision with another identical car that is moving west at 30 m/s and containing two large adults of equal mass.  The cars collide and stick together  and travel east at a speed of 5 m/s, how much do each of the adults weigh in newtons?

 

44.  How much work is required to increase the speed of a 40 kg object from 30 m/s to 50 m/s if:

For wimps:  the object is a block sliding on a friction free horizontal plane.

 

For the brave and reckless:  the object is a solid disk of radius 2 m rollling on a horizontal plane.  (5 pts Bonus!)

 

 

Bonus Problem #1  10 points

 Definitions:  Aft thrust engines propel a craft forward, forward thrust engines propel a craft backwards. 

A 104 kg space ship is moving forward at 60 m/s.  A 5 x 104 W forward thrust engine is employed for 30 seconds used to slow down the space ship. 

 

a.  What is the final velocity of the space ship?

b.  What was the total impulse delivered to the space craft ?

c.   What is the average force produced by the engine ?