Download Phys 201 Some problems for practice Dimensional Analysis 1) The

Phys 201
Some problems for practice
Dimensional Analysis
1) The position of a particle moving under uniform acceleration is some function of time
and the acceleration. Suppose we write this position s = kamtn, where k is a dimensionless
constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n =
2. Can this analysis give the value of k?
Kinematics
2) Kathy Kool buys a sports car that can accelerate at the rate of 4.90 m/s2. She decides to
test the car by racing with another speedster, Stan Speedy. Both start from rest, but
experienced Stan leaves the starting line 1.00 s before Kathy. If Stan moves with a
constant acceleration of
3.50 m/s2 and Kathy maintains an acceleration of 4.90 m/s2, find (a) the time at which
Kathy overtakes Stan, (b) the distance she travels before she catches him, and (c) the
speeds of both cars at the instant she overtakes him.
3) A student drives a moped along a straight road as described by the velocity-versustime graph in Figure P2.54. Sketch this graph in the middle of a sheet of graph paper.
(a) Directly above your graph, sketch a graph of the position versus time, aligning the
time coordinates of the two graphs. (b) Sketch a graph of the acceleration versus time
directly below the vx-t graph, again aligning the time coordinates. On each graph,
show the numerical values of x and ax for all points of inflection. (c) What is the
acceleration at
t = 6 s? (d) Find the position (relative to the starting point) at t = 6 s. (e) What is the
moped's final position at t = 9 s?
4) A ball is dropped from rest from a height h above the ground. Another ball is thrown
vertically upwards from the ground at the instant the first ball is released. Determine
the speed of the second ball if the two balls are to meet at a height h/2 above the ground.
Vectors
5) An airplane starting from airport A flies 300 km east, then 350 km at 30.0° west of
north, and then 150 km north to arrive finally at airport B. (a) The next day, another
plane flies directly from A to B in a straight line. In what direction should the pilot
travel in this direct flight? (b) How far will the pilot travel in this direct flight? Assume
there is no wind during these flights.
Two Dimensional Motion
6) A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the
goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high.
When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0° to
the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar?
(b) Does the ball approach the crossbar while still rising or while falling?
7) Figure P4.35 represents the total acceleration of a particle moving clockwise in a circle
of radius 2.50 m at a certain of time. At this instant, find (a) the radial acceleration, (b)
the speed of the particle, and (c) its tangential acceleration.
Relative Velocity
8) A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00
km and swims back to the starting point. If the student can swim at a speed of 1.20 m/s
in still water, how long does the trip take? Compare this with the time the trip would
take if the water were still.
Newton's Laws
9) The systems shown in Figure P5.21 are in equilibrium. If the spring scales are
calibrated in newtons, what do they read? (Neglect the masses of the pulleys and
strings, and assume the incline in part (c) is frictionless.)
10) A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that
passes over a pulley and then is fastened to a hanging 9.00-kg object, as in Figure P5.24.
Draw free-body diagrams of both objects. Find the acceleration of the two objects and
the tension in the string.
11) A 72.0-kg man stands on a spring scale in an elevator. Starting from rest, the
elevator ascends, attaining its maximum speed of 1.20 m/s in 0.800 s. It travels with this
constant speed for the next 5.00 s. The elevator then undergoes a uniform acceleration in
the negative y direction for 1.50 s and comes to rest. What does the spring scale register
(a) before the elevator starts to move? (b) during the first 0.800 s? (c) while the elevator
is traveling at constant speed? (d) during the time it is slowing down?
12) Three blocks are in contact with each other on a frictionless, horizontal surface, as in
Figure P5.54. A horizontal force F is applied to m1. If m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00
kg, and F = 18.0 N, draw a separate free-body diagram for each block and find (a) the
acceleration of the blocks, (b) the resultant force on each block, and (c) the magnitudes of
the contact forces between the blocks. (d) You are working on a construction project. A
coworker is nailing up plasterboard on one side of a light partition, and you are on the
opposite side, providing “backing” by leaning against the wall with your back pushing
on it. Every blow makes your back sting. The supervisor helps you to put a heavy
block of wood between the wall and your back. Using the situation analyzed in parts
(a), (b), and (c) as a model, explain how this works to make your job more comfortable.