Physics 101 - Final Exam 1997

Lecturer: D.S. Armstrong

Problem 1

 The speed v0 of a bullet (of mass m) is determined by shooting it into a block of wood (of mass M), which is suspended like a pendulum, and measuring the height h to which the pendulum rises. Consider the process in two stages: (i) the collision of the bullet and the block and (ii) the swing of the block (with embedded bullet). Hint: this should be familiar from the lab!
a) For each of the two stages (i) and (ii), state whether the mechanical energy of the system (mass m and mass M) is conserved.
b) Find an equation that gives v0 in terms of M , m , h , and g .
c) Find v0 given the values M = 1 kg, m = 10-2 kg, h = 20 cm, and g = 9.8 m/s2

Problem 2

Several children are pushing in different directions on a table. The (constant) force one child is exerting is F = (3i - 5j) N. The table undergoes a displacement of r = (2 i - 2 j ) m. Note: the displacement is not in the same direction as the force F , since other forces are acting on the table.
a) What is the work done by this child?
b) What is the angle between F and r ?

Problem 3

An object is projected from the surface of the Earth with a speed equal to twice the escape velocity. What is the speed of the object when it is very far from the Earth? Neglect air resistance. The radius of the Earth is 6370 km, and its mass is 5.98 x 1024 kg.

Problem 4

A block is made to oscillate vertically with a time dependence given by
y = (0.5) cos (2 t/2)
( y is in meters and t is in seconds).
a) What are the amplitude   A,  angular frequency     , and period   T   of the motion?
b) Write an expression for the velocity of the block   v(t) .
c) A penny is placed on top of the block. The frequency of the oscillation is kept constant, but the amplitude is increased. At what amplitude does the penny fly off the top of the block? g = 9.8 m/s2 .

Problem 5

A textbook, which has a mass of M = 0.5 kg, slides across a table. The coefficient of static friction between the book and the table is µs = 0.5 and the coefficient of kinetic friction is µk = 0.4 .
a) The initial speed of the book is vi = 3 m/s. Find the distance l that the book slides before coming to rest.
b) How long did the book take to slide the distance l ?

Problem 6

To start a playground merry-go-round rotating, a rope is wrapped around it and pulled. A force of 200 N is exerted on the rope for 10 seconds. During this time, the merry-go-round, which has a radius of 2 m, makes one complete rotation.
a) Find the angular acceleration of the merry-go-round, assuming it to be constant.
b) What is the magnitude of the torque exerted by the rope on the merry-go-round?
c) Assuming that the merry-go-round rotates in a clockwise manner, as viewed from above, in what direction is this torque vector?

Problem 7

Water (density = 1.00 x 103 kg/m3) is contained in a U-shaped tube with one end open, as shown. The water level differs by h = 5.0 m in the two arms.
a) If the gas pressure in the tube at point B is 1 atm (= 101.3 kPa), what is the gas pressure at point A?
b) If the liquid was gasoline (density = 0.68 x 103 kg/m3) instead of water, and the pressure at point A was the same as that calculated in part a), what would the level difference h be?

Problem 8

A pipe is closed at one end, and the other end is blocked by a piston of mass M = 1 kg. The piston is attached to a spring that has a force constant k = 100 N/m. The pipe is filled with water (bulk modulus B = 2.0 x 109N/m2, density = 1.00 x 103 kg/m3).
a) What is the speed of sound in the water inside the pipe?
b) What is the frequency at which the piston will oscillate on the spring?
c) What is the length of the shortest pipe such that there is a resonance between the sound waves in the water and the oscillations of the piston on the spring?

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last updated: Dec. 1 1998