Worked solutions Unit 3A
Contents

Fairground physics
E1

E2 A. Inside column, as a smaller distance is covered in the same time period, which means that the centripetal force is less on the small child
E3 Outside column, as a greater distance is covered in the same time period, which means that the centripetal force will be greater on the older child.
E4

E5

E6

E7

E8

E9

E10

E11

E12 Same maximum speed, as the mass of the car and riders cancels out of the equation.

E13

E14

E15

E16

E17

E18 A 2.00g ride can be created if the accelerating force is vertical as opposed to horizontal, for example a 2.00g force can be experienced at the bottom of a curve.
E19

E20

E21 a

b

E22

E23

E24

Power distribution and generation
E1

E2 a

b i ii The current in the secondary coil of a step-down transformer is always greater than the current in the primary coil, as current and voltage are inversely proportional in a transformation.
E3

Substituting into P = VI:

This is too large to run all these appliances at once; the extension cord on the power pack could heat up too much.

E4 a

b

c They should be able to use some appliances; however, lights would not be as bright, motors would not go as fast. Electronic devices may not function at all. d e

Chapter 1 Analysing motion
1.1 Projectile motion
1 a

b

c The only force acting on the ball is gravity, therefore the only acceleration is g = –9.80 m s–2. d e

2 a Horizontal velocity remains constant, so vx = 10.0 m s–1. b c

d

e

f

3 a

b c 4 a

b

c

5 a

b

c The acceleration of the ball is constant, due to gravity = –9.80 m s–2.
6 a At its maximum height, this is the point at which the ball has zero vertical velocity, while maintaining its horizontal velocity. b c d 7 a

b

c

8 C

9 a

b

c

d

e

f

g

10 a

b

c

1.2 Circular motion in a horizontal plane
1 a A, D b She has continued to travel in a straight line, while the car has turned, so the right side of the cabin is actually accelerating towards her.

2 a b c

3 a

b The force that causes the centripetal force is the reaction of the sideways frictional force of the car’s tyres on the road, that is the sideways force of friction of the road on the car’s tyres.
4 a b west
5 The car would probably skid off the road as the centripetal force required would increase to a value greater than the force of friction could provide.
6 a

b The forces are unbalanced as she is accelerating. According to Newton’s first law an unbalanced force will cause an object to change its motion, in this case the direction of the motion is changing, not the magnitude. c d The sideways reaction force of the skate on the ice, which is the sideways force of the ice on the skate.
7 a

b

c

d

e The force causing the centripetal acceleration of the ball is the tension force of the cable on the ball. f The ball would continue in a straight line that is tangential to the circular path at the point at which the wire breaks.

8 a

b The forces acting on Ella are gravity and the tension force of the rope on her. c Ella’s acceleration is towards the centre of rotation about the pole. d e

9 a

b

10 The driver will have to turn the car’s tyres down the track to enable the horizontal component of the sideways frictional force to help turn the car. The combined centripetal force of the banked track and the horizontal component of the sideways frictional force will enable the car to turn at this higher speed while maintaining the same radius as before.

1.3 Circular motion in a vertical plane
1 a The acceleration is towards the centre of the circular path of the yo-yo. b At