Physics 101 - Final Exam 1998

Lecturer: D.S. Armstrong

A coin of mass = 4 g lies on a copy of your physics textbook, which is being tilted at an angle with respect to the horizontal. The coefficient of static friction between the coin and the book is µ_s = 0.4 and the coefficient of kinetic friction is µ_k = 0.3.

a) Find the maximum angle at which the book can be tilted before the coin will start to slide.

b) Assume the book is tilted at an angle of 73°. What will be the kinetic energy of the coin after it has a slid a distance l = 15 cm along the cover of the book?

c) How long did it take for the coin to slide the distance l?

Problem 2

A child on rollerblades catches a ball that has a mass of m₁ = 0.25 kg. The initial velocity of the ball is v₁ = (10 m/s)i and the initial velocity of the child is zero. The mass of the child (including her rollerblades) is m₂ = 30 kg. Ignore gravity and air resistance.

a) What is the velocity of the child immediately after she catches the ball?

b) What is the change in the total mechanical energy when the child catches the ball?

Problem 3

An object is projected from the surface of the Earth with an initial speed equal to three times 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, its mass is 5.98 x 10²⁴ kg, G = 6.67 x 10^-11 N m²/ kg².

Problem 4

A flagpole of mass m and length L is hinged at a wall and supported in a horizontal position by a massless cable attached to the free end (see diagram). The cable makes an angle with the horizontal.

a) What is the tension in the cable?

b) What is the (vector) force exerted on the flagpole by the hinge?

c) What is the direction of the torque (about the hinge point) that the tension in the cable exerts on the flagpole?

Problem 5

A transverse wave has the form

y = 10 sin(0.01x - 20t)

where x, y have units of meters, and t has units of seconds.

a) What is the wavelength and frequency of this wave?

b) What is the magnitude and direction of the wave velocity?

c) What is the value of y for x = 20 m at time t = 0.05 s?

d) What are the maximum values of dy/dt and dy/dx ?

Problem 6

A police car, travelling at 120 km/hr, passes a pedestrian. The siren is on, emitting a sound of frequency 360 Hz. What is the frequency of the sounds the pedestrian hears

a) when the police car is approaching the pedestrian?

b) when the car is receding from the pedestrian?

Problem 7

A cylindrical rod is formed from cork (specific gravity = 0.25) and aluminum (specific gravity = 2.7) cylindrical sections. The lengths of the sections are 20.0 cm and 1.0 cm respectively. The rod is allowed to float in Lake Matoaka, with the heavy end downwards.

a) In equilibrium, how much of the cylinder's length is underwater?.

b) [Extra credit question - do not attempt this part unless you have finished the rest of the exam!] The cylinder is given a push, so that it begins to bob up-and-down in the water. What is the frequency of the resulting oscillation?

Problem 8

The polar ice caps of the earth contain 2 x 10¹⁹ kg of ice. Since this ice is located at the poles, its contribution to the moment of inertia of the earth is negligible. In a weird practical joke, the Klingon empire arranges to have all of this ice moved to a single pile located on the equator. The radius of the Earth = 6370 km, the mass of the Earth = 6.0 x 10²⁴ kg, I_sphere = (2/5)MR².

a) Would the length of the day become shorter or longer? Why?

b) By how much?