University of Cape Town
Department of Physics
Weekly Problem Set 9
Wednesday 14 April 2010
Read these instructions very carefully: You have been assigned to a group of 3 for the duration of this tutorial.
Work together on the problems below and call a tutor if needed. Each student needs to be working on paper
during this time. Each student then must hand in individual, full solutions before 10:00 a.m. on Wednesday 21
April into the special box in the Course I laboratory. Your marked tutorials will be returned in the PHY1023H
pigeonholes and solutions will go up on the notice board.
1. Determine the (indefinite) integrals of the following functions:
(a) 9 x (b) 5 x2 (c) x4 / 5 (d) 7 (e) x-3 (f) 7 x2 + 2 x.
2. Shown is a force-distance graph for a constantly decreasing (N)
force acting on a mass moving in the x-direction. 40
(a) From the graph, calculate how much work is done by this force 30
in moving the mass from point A to point B.
(b) Write down the integral (with the appropriate numerical values)
that will enable you to calculate the work done by the force in
moving the block from A to B.
(c) Solve the integral. 10
Do you get same answer as you got in (a)?
0 15 20
3. Consider the lines below which mark the paths of a moving particle.
A B C D E F
(a) Which paths describe motion in one dimension?
(b) Which paths describe motion in two dimensions?
(c) Which paths could be used to describe motion having constant velocity?
(d) Which paths could be used to describe motion having acceleration (change in velocity?)
4. Look at the picture alongside. It shows photographs taken of
two balls: one is projected horizontally at some height, and at
the same time a second ball is dropped from rest from the same
height. Both balls fall under the influence of gravity. Look
carefully at the picture. What can you conclude about the
motion of the two balls? Does your conclusion depend on how
fast the one ball is projected horizontally?
5. In each situation below, photographs were taken of a ball as it moved from its starting position
(shown shaded) to its final position (shown solid). The photographs were taken the same time apart
and superimposed on top of each other in each of the frames below.
A B C D
(a) Copy these pictures on your page and add in a continuous line representing the path of the ball. How
sure are you of your answers in each case?
(b) Which pictures could be describing motion in one dimension?
(c) Which pictures could be describing motion in two dimensions?
(d) Which pictures could be describing motion having constant velocity?
(e) For each picture, describe (in words) what might have been photographed. In other words, describe
the motion of the ball in each case.
6. For each of the situations below, (i) draw the “freeze frame” representation (ii) draw in velocity
vectors at each of the position of the photograph, and (iii) indicate the direction of the acceleration.
Label your diagrams clearly. Draw the lift as a circle.
(a) A lift moving up with constant velocity
(b) A lift going up and speeding up.
(c) A lift going down and speeding up.
(d) A lift moving up and slowing down.
(e) A lift going down and slowing down.
7. For one region of an engine cycle, the pressure P of the gas in the engine cylinder is related to the
volume V by
P=5V + 3 where the volume is in m3 and the pressure in pascals.
(a) Draw a rough graph of this relationship
(b) Using your graph, determine how much work is done when the volume of the cylinder is increased
from 0.4 m3 to 0.9 m3.
(c) Calculate the work done when the volume of the cylinder is increased from 0.4 m3 to 0.9 m3 using an
integral. Compare your answer to (b)
(d) Explain carefully the physical meaning of the integral.