Scalar and vector quantities

A scientist uses a rocket to study the Earth’s atmosphere.

The scientist launches the rocket from rest at the point A at t = 0 seconds. The force produced by the rocket’s engine causes it to accelerate.

At t = 50 seconds, the rocket’s engine no longer produce an accelerating force as all of the fuel has been used. The rocket has reached point B. Its velocity is now 3.1 km s^–1 at an angle of 75° to the horizontal.

The rocket engine works by expelling hot gas backwards.

Explain, using Newton’s laws of motion, how the engine causes the rocket to accelerate between t = 0 and t = 50 s.

Suggest why the magnetic force acting on the proton has a different magnitude at X than at Y

At X, the motion of the proton is instantaneously equivalent to motion in a circle at a constant speed.

Calculate the radius of this circular motion.

1 Calculate the magnitude of the resultant force on the proton at Y.

2 Explain why the motion of the proton at Y is not instantaneously equivalent to motion in a circle at a constant speed.

Which row contains only scalar quantities?

A Absolute temperature, displacement, moment

B Acceleration, force, momentum

C Gravitational potential, kinetic energy, mass

D Kinetic energy, mass, momentum

Your answer

Draw an arrow labelled T on the diagram to represent the tension in the rod.

Show that the radius of the circular path followed by the sandbag is about 10 m.

Calculate the tension T in the rod.

Show that the angular velocity of the ride is about 0.8 radians per second.

When the seat is at its highest point the sandbag is 17 m above the ground. The sandbag is released from the seat to model an object being dropped by a rider.

Calculate t, the time taken for the sandbag to reach the ground.

Using your answer to (a)(iv), determine the horizontal displacement s travelled by the sandbag before hitting the ground.

Determine, with reasons, the effect on the horizontal displacement travelled if the object released from the ride was a shoe from a rider.

A truck pulls a car up a slope at a constant speed. The truck and the car are joined with a steel tow bar, as shown in the diagram.

The diagram is not drawn to scale.

The slope is 10 to the horizontal ground. The mass of the car is 1100 kg. The car travels from A to B. The vertical distance between A and B is 120 m.

There are four forces acting on the car travelling up the slope.

Complete the free-body diagram below for the car and label the missing forces.

Show that the component of the weight of the car W_s acting down the slope is about 1900 N.

The total frictional force acting on the car as it travels up the slope is 300 N.

Calculate the force provided by the tow bar on the car.

The steel tow bar used to pull the car has length 0.50 m and diameter 1.2 × 10^–2 m. (e) The Young modulus of steel is 2.0 × 10¹¹ Pa.

Calculate the extension x of the tow bar as the car travels up the slope.

An archer fires an arrow towards a target as shown below.

The diagram is not drawn to scale.

The centre of the target is at the same height as the initial position of the arrow. The target is a distance of 90 m from the arrow. The arrow has an initial velocity of 68 m s^–1 and is fired at an angle of 11 to the horizontal.

Air resistance has negligible effect on the motion of the arrow.

Describe how the kinetic energy of the arrow changes during its journey from when it is fired until it reaches its maximum height.

Show that the time taken for the arrow to reach its maximum height is about 1.3 s.

The arrow misses the target.

Calculate the horizontal distance, measured along the base line, by which the arrow misses the target.

Explain what is meant by an inelastic collision.

The target is mounted on wheels. The target has a much larger mass than the mass of the arrow.

Using ideas of momentum, explain the velocity of the target immediately after the arrow sticks into the target.

The diagram below shows the arrangement of the 3 protons inside the nucleus of lithium-6

The separation between each proton is about 1.0 × 10⁻¹⁵ m.

Calculate the magnitude of the repulsive electric force F experienced by the proton P

Explain how protons stay within the nucleus of lithium-6.

A spherical metal dome shown below is charged to a potential of −12 kV.

The dome is supported by a cylindrical plastic rod. The radius of the dome is 0.19 m.

Show that the magnitude of the total charge Q on the dome is 2.5 × 10⁻⁷ C.

The dome discharges slowly through the plastic rod. It takes 78 hours for the dome to completely discharge.

1 Show that the mean current I in the plastic rod is about 9 × 10⁻¹³ A.

2 The average potential difference across the plastic rod during discharge is 6000 V. The rod has cross-sectional area 1.1 × 10⁻⁴ m² and length 0.38 m.

Calculate the resistivity of the plastic.

=........ m

At an airport, the conveyor belt for suitcases moves at a constant speed of 1.5 m s^–1. In Fig. 4.1, a suitcase of mass 8.0 kg has reached the line labelled XX'.

Fig. 4.2 shows the situation in vertical cross-section. The frictional force F prevents the suitcase of weight W from sliding to the bottom of the belt. The normal contact force on the suitcase is R. The belt is inclined at an angle of 30° to the horizontal.

Fig. 4.3 shows the suitcase and the forces acting on it at the line labelled YY'.

The centre of mass of the suitcase is now moving at 1.5 m s^–1 along a semi-circular arc of radius 2.0 m.

Calculate the magnitude of the centripetal force acting on the suitcase.

When the suitcase is at line YY', the magnitude of force F is larger and the magnitude of force R is smaller than at XX'.

Explain why this is so.