Tutorial 1 Taken from Lecture : )

GEK1521 / PC1326 Tutorial 1 ( Lecture 1-4: Units, Vectors & Mechanics )
1. When a sphere moves through a fluid slowly, it usually experiences a drag force. This force is determined by the radius of the sphere r, the speed of the sphere v, and the viscosity of the fluid  (in the unit of [kg/(m∙s)]). Using dimensional analysis, determine how the force depends on these factors.

2. Three vectors A, B, and C add together to yield zero: A + B + C = 0. The vectors A and C point in opposite directions and their magnitudes are related by the expression: A = 2C. Which one of the following conclusions is correct? a) b) c) d) e) A and B have equal magnitudes and point in opposite directions. B and C have equal magnitudes and point in the same direction. B and C have equal magnitudes and point in opposite directions. A and B point in the same direction, but A has twice the magnitude of B. B and C point in the same direction, but C has twice the magnitude of B.
B 6.4 m 5.4 m

3. A toolbox is carried from the base of a ladder at point A to a scaffold 5.0 m above the ground at point B as shown in the figure. What is the magnitude of the displacement of the toolbox in its movement from point A to point B? a) b) c) d) e) 15 m 19 m 8.1 m 11 m 13 m

7.6 m 6.6 m

A

4. Given mass m, height h, gravitational acceleration constant g, time t, which one of the following is a dimensionless parameter? a) mg/ht b) h/gt c) h/gt2 d) mh/gt2 e) mh/gt

5. A ball hangs from a string attached to the ceiling. What is the net force acting on the ball? a) The net force is downward. b) The net force is upward. c) The net force is zero.

6. You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. In the reference frame of the ground, which of the following is correct? a) b) c) d) e) A net force acted on it. No net force acted on it. It remained at rest. It did not move, but only seemed to. Gravity briefly stopped acting on it.

7. Consider a cart on a horizontal frictionless table. Once the cart has been given a push in the x-direction and released, what will happen to the cart? a) b) c) d) e) It slowly comes to a stop. It continues with constant acceleration. It continues with decreasing acceleration. It continues with constant velocity. It immediately comes to a stop.

8. Off to the Races:

F v
From rest, we step on the gas of our Ferrari, providing a force F for 4s, speeding it up to a final speed v. If the applied force were only 1/2 F, how long would it have to be applied to reach the same final speed? a) 16s b) 8s c) 4s d) 2s e) 1s

9. Two blocks of the same mass are connected by a string and are pulled across a frictionless surface by a constant force. Will the two blocks move with constant velocity?

a) Yes, both blocks move with constant velocity. b) No, both blocks move with constant acceleration. c) The two blocks will have different velocities and/or accelerations.

10. Referring to figure in Q9, will the tension in the connecting string be greater than, less than, or equal to the force F ? a) Greater than. b) Less than. c) Equal to.

11. Force and Two Masses:

F

m1

a1 a2 = 2a1

F

m2

F

m2 m1

a3

A force F acts on mass m1 giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2 = 2a1. If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration? a) 3/4 a1 b) 3/2 a1 c) 1/2 a1 d) 4/3 a1 e) 2/3 a1

12. Bowling vs. Ping-Pong I:

F12

F21

In outer space, a bowling ball and a ping-pong ball attract each other due to gravitational forces. How do the magnitudes of these attractive forces compare? a) b) c) d) e) The bowling ball exerts a greater force on the ping-pong ball. The ping-pong ball exerts a greater force on the bowling ball. The forces are equal in magnitude. The forces are zero because they cancel out. There are actually no forces at all.

13. Bowling vs. Ping-Pong II: In outer space, gravitational forces exerted by a bowling ball and a ping-pong ball on each other are equal and opposite. How do their accelerations compare? a) b) c) d) e) They do not accelerate because they are weightless. Accelerations are equal, but not opposite. Accelerations are opposite, but bigger for the bowling ball. Accelerations are opposite, but bigger for the ping-pong ball. Accelerations are equal and opposite.

14. A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?

T v
a) Tension does no work at all. b) Tension does negative work. c) Tension does positive work.

15. You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book?

r

FHAND v = const a=0 mg

a) b) c) d) e)

mg  r FHAND  r (FHAND + mg)  r Zero None of the above.

16. Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? a) b) c) d) e) The same as the short path. Twice as much. Four times as much. Half as much. No PE gained in either case.

17. A hole is drilled through the center of Earth and emerges on the other side. You jump into the hole. What will happen to you? (Hint: Inside earth, when you are at a distance r away from the center, the gravitational force on you is just the force due to your body mass and the earth mass of sphere of radius r from the center.)

a) b) c) d)

You fall to the center and stop. You go all the way through and continue off into space. You fall to the other side of Earth and then return. You won’t fall at all.

18. A proton and an electron are held apart a distance of 1 m and then released. As they approach each other, what will happen to the force between them? a) It gets bigger. b) It gets smaller. c) It stays the same.

19. Continuing from Q18, which particle has the larger acceleration at any time? a) Proton. b) Electron. c) Both the same.

20. Continuing from Q19, where would they meet? a) In the middle. b) Closer to the electron’s side. c) Closer to the proton’s side.

21. Considering a vibrating pendulum as shown in the figure.

i) At which of the above time is the kinetic energy a maximum? ii) At which of the above time is the potential energy a maximum? iii) At which of the above time is kinetic energy being transformed to potential energy? iv) At which of the above time is potential energy being transformed to kinetic energy?