pt3sem-12014key__ap

2014-15 / Semester 1 / Final Exam Prep

AP Physics Practice Exam #3 Name: KEY (Solutions) Hour: Date Ass’d:

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Practice Exam #3 ____ /

Free Response 6 Q's / 90 min. / Yellow, Green, Calculator

2007/M1. A block of mass m is pulled along a rough horizontal surface by a constant applied force of

magnitude F1 that acts at an angle to the horizontal, as indicated above. The acceleration of the block is a1 . Express all algebraic answers in terms of m, F1 , , a1 , and fundamental constants.

(a) On the figure below, draw and label a free-body diagram showing all the forces on the block. (b) Derive an expression for the normal force exerted by the surface on the block.



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(c) Derive an expression for the coefficient of kinetic friction µ between the block and the surface. (d) On the axes below, sketch graphs of the speed v and displacement x of the block as functions of

time t if the block started from rest at x = 0 and t = 0.

(e) If the applied force is large enough, the block will lose contact with the surface. Derive an expression for

the magnitude of the greatest acceleration amax that the block can have and still maintain contact with

the ground.



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1984/M3. A small body of mass m located near the Earth’s surface falls from rest in the Earth's gravitational field. Acting on the body is a resistive force of magnitude k m v, where k is a constant and v is the speed of the body. (a) On the diagram below, draw and identify all of the forces acting on the body as it falls.

(b) Write the differential equation that represents Newton's second law for this situation. (c) Determine the terminal speed vT of the body.



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(d) Integrate the differential equation once to obtain an expression for the speed v as a function of time t . Use the condition that v = 0 when t = 0. (e) On the axes provided below, draw a graph of the speed v as a function of time t .



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1998/M3. Block 1 of mass m1 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. (a) 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

m1

ii. The friction force f1 exerted on block 1 by block 2 m1



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iii. The force T exerted on block 2 by the string m2

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

m2

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

m2

(b) Determine the largest value of M for which the blocks can remain at rest.



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(c) 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.



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(d) 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



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2012 AP-B Practice Exam / #1. The experimental apparatus shown in the figure above contains a pendulum consisting of a 0.66 kg ball attached to a string of length 0.60 m. The pendulum is released from rest at an angle of 60° and collides with a ball of mass 0.22 kg initially at rest at the edge of a table. The 0.22 kg ball hits the floor a distance of 1.4 m from the edge of the table.

(a) Calculate the speed of the 0.66 kg ball just before the collision.

(b) Calculate the speed of the 0.22 kg ball immediately after the collision.



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(c) Calculate the speed of the 0.66 kg ball immediately after the collision.

(d) Indicate the direction of motion of the 0.66 kg ball immediately after the collision.

____ To the left ____ To the right

(e) Calculate the height to which the 0.66 kg ball rises after the collision.

(f) Based on your data, is the collision elastic?

____ Yes ____ No

Justify your answer.



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1993/M1. A massless spring with force constant k = 400 N/m is fastened at its left end to a vertical wall, as shown in Figure 1. Initially, block C (mass m0 = 4.0 kg) and block D (mass mD = 2.0 kg) rest on a horizontal

surface with block C in contact with the spring (but not compressing it) and with block D in contact with block C. Block C is then moved to the left, compressing the spring a distance of 0.50 m, and held in place while block D remains at rest as shown in Figure 11. (Use g = 10 m/s2.)

(a) Determine the elastic energy stored in the compressed spring. Block C is then released and accelerates to the right, toward block D. The surface is rough and the coefficient of friction between each block and the surface is = 0.4. The two blocks collide instantaneously, stick together, and move to the right. Remember that the spring is not attached to block C. Determine each of the following: (b) The speed vc of block C just before it collides with block D



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(c) The speed vf blocks C and D just after they collide

(d) The horizontal distance the blocks move before coming to rest



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1976/M1. A small block of mass m slides on a horizontal frictionless surface as it travels around the inside

of a hoop of radius R. The coefficient of friction between the block and the wall is ; therefore, the speed v of the block decreases. In terms of m, R, , and v, find expressions for each of the following. (a) The frictional force on the block (b) The block's tangential acceleration dv/dt (c) The time required to reduce the speed of the block from an initial value v to v/3

pt3sem-12014key__ap

Documents

block of mass

key solutions hour

friction force f1

date assd

small body of mass

mass m1

resistive force of magnitude

normal force n1

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