Física

Thompkins
AP Physics Mid-term Exam Review

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1) 1979M1. A ball of mass m is released from rest at a distance h above a frictionless plane inclined at an angle of 45° to the horizontal as shown above. The ball bounces elastically off the plane at point P1 and strikes the plane again at point P2. In terms of g and h determine each of the following quantities:
a. The velocity (a vector)of the ball just after it first bounces off the plane at P1.
b. The time the ball is in flight between points P1 and P2.
c. The distance L along the plane from P1 to P2.
d. The speed of the ball just before it strikes the plane at P2.
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2) 1979M2. A ferryboat of mass M1 = 2.0 x 105 kilograms moves toward a docking bumper of mass M2 that is attached to a shock absorber. Shown below isa speed v vs. time t graph of the ferryboat from the time it cuts off its engines to the time it first comes to rest after colliding with the bumper. At the instant it hits the bumper, t = 0 and v = 3 meters per second.
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a. After colliding inelastically with the bumper, the ferryboat and bumper move together with an initial speed of 2 meters per second. Calculate the mass of the bumperM2.
b. After colliding, the ferryboat and bumper move with a speed given by the expression v = 2e-4t. Although the boat never comes precisely to rest, it travels only a finite distance. Calculate that distance.
c. While the ferryboat was being slowed by water resistance before hitting the bumper, its speed was given by 1/v = 1/3 + (t, where ( is a constant. Find an expression for the retardingforce of the water on the boat as a function of speed.






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3) 1983M1. A particle moves along the parabola with equation y = 2x2 shown above.
a. Suppose the particle moves so that the x-component of its velocity has the constant value vx = C; that is, x = Ct
i. On the diagram above, indicate the directions of the particle's velocity vector v and acceleration vector a atpoint R, and label each vector.
ii. Determine the y-component of the particle's velocity as a function of x.
iii. Determine the y-component of the particle's acceleration.








b. Suppose, instead, that the particle moves along the same parabola with a velocity whose x-component is given by vx = C/(1+x²)½
i. Show that the particle's speed is constant in this case.ii. On the diagram below, indicate the directions of the particle's velocity vector v and acceleration
vector a at point S, and label each vector. State the reasons for your choices.







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1992M1. A ball of mass 9m is dropped from rest from a height H = 5.0 meters above the ground, as shown above on the left. It undergoes a perfectly elastic collision with the groundand rebounds. At the instant that the ball rebounds, a small blob of clay of mass m is released from rest from the original height H, directly above the ball, as shown above on the right. The clay blob, which is descending, eventually collides with the ball, which is ascending. Assume that g = 10 m/s2, that air resistance is negligible, and that the collision process takes negligible time.
a.Determine the speed of the ball immediately before it hits the ground.
b. Determine the time after the release of the clay blob at which the collision takes place.
c. Determine the height above the ground at which the collision takes place.
d. Determine the speeds of the ball and the clay blob immediately before the collision.
e. If the ball and the clay blob stick together on impact, what isthe magnitude and direction of their velocity immediately after the collision?


5) 1984M3. 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 kmv, 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...