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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....
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