AP Physics: Friction and Circular Motion · Name: _____ 5 A small block of mass MB = 0.50 kg is placed on a long slab of mass MS = 3.0 kg as shown above. Initially, the slab is at

Name: ________________________________________________ Assignment Due Date: January 9, 2012

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AP Physics: Friction and Circular Motion

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. An object moves in a circle counterclockwise with constant speed. Which figure shows the correct velocity and acceleration vectors?

a. c.

b. d.

____ 2. A car speeds along the curved exit ramp of a freeway. The radius of the curve is 80 m. A 70-kg passenger holds the arm rest of the car door with a 220-N force to keep from sliding across the front seat of the car. (Assume that the exit ramp is not banked and ignore friction with the car seat.) What is the car's speed?a. 16 m/s d. 50 m/sb. 57 m/s e. 28 m/sc. 18 m/s

Name: ________________________

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Problem

Block 1 of mass ml is placed on block 2 of mass m2 which is then placed on a table. A string connecting block 2 to a hanging mass M passes over a pulley attached to one end of the table, as shown above. The mass and friction of the pulley are negligible. The coefficients of friction between blocks 1 and 2 and between block 2 and the tabletop are nonzero and are given in the following table.

Express your answers in terms of the masses, coefficients of friction, and g, the acceleration due to gravity.

3. Suppose that the value of M is small enough that the blocks remain at rest when released. For each of the following forces, determine the magnitude of the force and draw a vector on the block provided to indicate the direction of the force if it is nonzero.

i. The normal force N1 exerted on block 1 by block 2

Name: ________________________

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ii. The friction force f1 exerted on block 1 by block 2

iii. The force T exerted on block 2 by the string

iv. The normal force N2 exerted on block 2 by the tabletop

v. The friction force f2 exerted on block 2 by the tabletop

Name: ________________________

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4. Determine the largest value of M for which the blocks can remain at rest.

5. Now suppose that M is large enough that the hanging block descends when the blocks are released. Assume that blocks 1 and 2 are moving as a unit (no slippage). Determine the magnitude a of their acceleration.

6. Now suppose that M is large enough that as the hanging block descends, block 1 is slipping on block 2. Determine each of the following.

i. The magnitude a1 of the acceleration of block 1

ii. The magnitude a2 of the acceleration of block 2

Name: ________________________

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A small block of mass MB = 0.50 kg is placed on a long slab of mass MS = 3.0 kg as shown above. Initially, the slab is at rest and the block has a speed vo of 4.0 m/s to the right. The coefficient of kinetic friction between the block and the slab is 0.20, and there is no friction between the slab and the horizontal surface on which it moves.

7. On the dots below that represent the block and the slab, draw and label vectors to represent the forces acting on each as the block slides on the slab.

8. At some moment later, before the block reaches the right end of the slab, both the block and the slab attain identical speeds vf .

Calculate vf .

Name: ________________________

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9. Calculate the distance the slab has traveled at the moment it reaches vf .

10. A boy whirls a ball on a string in a horizontal circle of radius 0.8 m. How many revolutions per minute must the ball make if the magnitude of its centripetal acceleration is to be the same as the free-fall acceleration due to gravity g?

11. Mass m1 moves with speed v in a circular path of radius R on a frictionless horizontal table as shown in the figure below. It is attached to a string that passes through a frictionless hole in the center of the table. A second mass m2 is attached to the other end of the string. Derive an expression for R in terms of m1, m2, and v.

Name: ________________________

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12. A 100-g disk sits on a horizontally rotating turntable. The turntable makes one revolution each second. The disk is located 10 cm from the axis of rotation of the turntable. (a) What is the frictional force acting on the disk? (b) The disk will slide off the turntable if it is located at a radius larger than 16 cm from the axis of rotation. What is the coefficient of static friction?

ID: A

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AP Physics: Friction and Circular Motion

Answer Section

MULTIPLE CHOICE

1. ANS: C REF: Tipler4thed.p.142#44 2. ANS: A REF: Tipler4thed.p.145#70

ID: A

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PROBLEM

3. ANS:

REF: Free Resp Ques 1998 Mech #3a 4. ANS:

REF: Free Resp Ques 1998 Mech #3b

ID: A

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5. ANS:

REF: Free Resp Ques 1998 Mech #3c

ID: A

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6. ANS:

REF: Free Resp Ques 1998 Mech #3d

ID: A

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7. ANS:

REF: AP Physics Final 2006 Free Resp (Mech) #1a

ID: A

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8. ANS:

ID: A

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REF: AP Physics Final 2006 Free Resp (Mech) #1b

ID: A

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9. ANS: Momentum approach to part (b); Newton's second law and kinematics approach to part (c)

Newton's second law and kinematics approach to part (b): kinematics approach to part (c)

REF: AP Physics Final 2006 Free Resp (Mech) #1c 10. ANS:

REF: Tipler4thed.p.142#47

ID: A

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11. ANS:

REF: Tipler4thed.p.143#53 12. ANS:

REF: Tipler4thed.p.144#60