Coursework 3 (11 questions) NU-CPS Physics 2014-15

INTRODUCTION TO MECHANICS. FORCES. NEWTON’S LAWS.

1) The London Eye has a diameter of 135 m and turns one revolution in 30.0 minutes. You are in a capsule moving around. You enter at the bottom and after 15.0 minutes you are at the top. Calculate (a) your average speed, (b) your average velocity, (c) your change in velocity. (6 marks)

2) a) Use the equations and to derive (or prove) the other equations used to solve problems of constant acceleration. (The SUVAT Equations).

b) The value of the acceleration due to gravity, g, can be calculated by observing the vertical motion of a ball as it goes up and down. Two detectors measuring time are separated by a vertical distance h. A ball is projected upwards and during its flight passes both detectors twice. If the ball is above the lower detector for a time T₁ and above the upper detector for a time T₂, derive an expression for g in terms of h, T₁ and T_{2 .} (3 marks)

3) A football player kicks a ball from the ground at an angle of 36.0º from the horizontal with an initial speed of 15.5 m s^-1. It hits the goal post at a height of 1.85 m. What is the longest possible distance between the player and the goal? (Note: This involves quadratics. Clearly show your work) (6 marks)

4) A particle accelerates from rest at O and moves along the x-axis. During the first 3.00 s, it accelerates uniformly at 2.00 m s^-2. Then its acceleration instantaneously increases by 100% and it accelerates until it reaches a speed of 30.0 m s^-1. For the next 10.0 s, it moves at constant speed before decelerating uniformly, coming to rest after a further T seconds.

a) Display this information in a speed-time graph.

b) Given that the total distance travelled is 477 m, calculate T. (4 marks)

5) A steel ball, a table tennis ball and a person fall at the same time out of an aeroplane. Their terminal speeds are 80.0 m s^-1, 5.00 m s^-1 and 70.0 m s^-1 respectively. Draw a speed-time graph including all three falling objects. Ensure the graph is to scale. (4 marks)

Pushing Force

6) Consider a block (initially at rest) of mass 5.00 kg on a frictionless table top. Let a pushing force of 50.0 N directed at an angle of 30.0° below the horizontal act on the block.

a) Find the acceleration of the block.

m

b) Find the (normal) force that the table

exerts on the block.

(8 marks)

7) Five identical cubes, each of mass m, lie on a straight line, with their adjacent faces in contact on a horizontal surface as shown:

Suppose the surface is frictionless and that a constant force P is applied from left to right to A as shown.

a) What is the acceleration of the system?

b) What is the resultant force acting on each cube?

c) What force does cube C exert on cube D? (6 marks)

8) A parachutist jumps from a plane at time t = 0. After 8.00 s, he reaches terminal velocity and after another 5.00 s, he opens his parachute. He lands at t = 30.0 s. a) Draw a velocity-time graph of his motion.

b) Describe the forces acting on the parachutist during his fall.

9) A small rocket is fired vertically upwards from ground level. The graph below shows how the upward speed of the rocket changes with time. The rocket burns fuel at a constant rate for several seconds and then, as the fuel runs out, the rate of burning decreases to zero in a second or two. The rocket goes straight up.

a) Sketch a graph to show approximately how the acceleration of the rocket varies during the time to . b) Explain how it is possible for the acceleration to increase while the fuel is burning at a constant rate. c) Why is the portion of the graph from time to time straight? d) At which of the times identified on the time axis was the resultant force on the rocket equal to zero? Explain your answer.

(8 marks)

10) The diagrams below show a sphere, S, at equilibrium on a table (left) and a free-body diagram (right) on which the forces (P and Q) acting on the sphere have been marked. Force P represents the weight of the sphere and force Q represents the reaction of the table.

According to Newton’s 3^rd law, forces only occur in pairs.

a) On what body does the force which pairs with force Q act? Give its direction.

b) On what body does the force which pairs with force P act? Give its direction.

c) Let two forces, F₁ and F₂, be a Newton 3^rd law pair. State one way in which these two forces are different and one way in which they are similar. (4 marks)

11) A large cardboard box of mass m = 1.50 kg is pulled across a horizontal floor by a force F of magnitude 9.00 N. The motion of the box is opposed by a constant frictional force F_R of magnitude 1.50 N between the box and the floor, and an air resistance force F_A whose magnitude can be expressed as , where k = 6.00 × 10^-2 kgm^-1 is a constant and v is the velocity of the box. Assuming that the direction of F_R and F_A is opposite to the direction of motion of the box:

a) sketch a diagram showing the directions of all the forces acting on the moving box

b) calculate the maximum acceleration of the box

c) calculate the maximum speed of the box. (6 marks)

Numerical Answers to CW3

1. a.) 0.236 m/s, b.) 0.150 m/s (upwards), c.) 0.472 m/s (to the right)

2. These are Proofs and have no numerical answers. HINT: they start with the lecture given definitions of acceration, <v>, and displacement.

3. 20.4 m

4.

b) T= 4.00 s

a)

5. Graph

6. a) a = 8.66 m/s² , b) N = 74.1 N

7. a.) P/5m, b.) P/5, c.) 2P/5

8. a) Graph b) Description – no numbers

9. Graph

10. a) downward, b) Upward from center of Earth

11. a.) Diagram, as per lecture b.) 5.00 m/s², c.) 11.2 m/s²

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