Gravity & weight

A washing machine with a circular drum of diameter 0.60 m is rotating at an angular velocity of 15 radians per second.

What is the magnitude of the force exerted by the drum on a 0.30 kg item of clothing which is at the bottom of the spinning drum?

A 21 N

B 23 N

C 41 N

D 43 N

A sealed container contains n moles of an ideal gas. The gas has pressure p, absolute temperature T and occupies volume V.

The mass of one mole of the gas is M.

Use an ideal gas equation to show that the density of the gas is given by the expression

An airship has a cabin suspended underneath a gasbag inflated with helium.

The airship is floating above the ground and is stationary.

The volume of the gasbag is 12 000 m³. The temperature of the helium and the surrounding air is 20 °C. Atmospheric pressure is 1.0 × 10⁵ Pa. The molar mass of air is 0.029 kg mol^–1. The volume of the cabin is negligible compared to the volume of the gasbag.

Show that the density of air under the conditions described is about 1.2 kg m^–3. (i)

Calculate the weight of air displaced by the airship.

weight of air........ N

Explain why the weight of air displaced by the airship has the same magnitude as the weight of the airship and its contents.

The pressure of the helium in the gasbag is maintained at a value only slightly greater than atmospheric pressure. Suggest why a larger pressure is not used.

The airship engine drives a fan which moves 7.8 kg of air per second at a relative speed of 45 m s^–1, so the airship starts to move.

All other conditions given in (b) remain the same.

Calculate the thrust that the engine produces.

The airship has a higher maximum speed at high altitudes, but also produces less thrust from the engine.

Explain these observations.

A student uses a motion-sensor connected to a laptop to investigate the motion of a hollow ball of mass 1.2 × 10^–2 kg falling through air.

The ball is dropped from rest. It reaches terminal velocity before it reaches the ground.

The upthrust on the ball is negligible.

Fig. 17 shows the variation with time t of the velocity v of the ball as it falls towards the ground.

Draw a tangent to the curve at t = 0.25 s and determine the acceleration of the ball.

acceleration =........ m s^–2

Calculate the resultant force F acting on the ball at t = 0.25 s.

Use your answer in (b) to calculate the drag on the ball at time t = 0.25 s.

The student now adds a small amount of sand inside the hollow ball. As before, the ball is dropped from rest and it also reaches terminal velocity before it reaches the ground.

Describe how the forces acting on the sand-filled ball at v = 0.50 m s^–1 compare with the forces acting on the hollow ball at this speed.

Explain why the terminal velocity of the sand-filled ball will be greater than the terminal velocity of the hollow ball.

A screw is used to hang a wooden sign on a wall. It is screwed into the wall using a screwdriver.

The width of the screwdriver blade is 5.0 × 10^–3 m from end to end. (a) The ends of the blade exert equal and opposite forces on the screw. The magnitude of each force is 350 N, as shown in Fig. 22.1.

Calculate the magnitude of the torque of the couple produced by the forces at each end of the screwdriver blade.

torque =........ N m

The wooden sign is then hung on the screw at point A. The forces acting on the screw are shown in Fig. 22.2.

The inside section of the wall exerts a maximum downwards force of 31 N at a distance of 3.0 × 10^–2 m from the outer edge of the wall. The hanging wooden sign exerts a force F at a distance 7.0 × 10^–3 m from the outer edge of the wall. There is a force R acting on the screw at the outer edge of the wall. The mass of the screw is negligible.

Use the principle of moments to calculate the maximum mass of the wooden sign.

A toy rocket is made from a 1.5 litre plastic bottle with fins attached for stability.

The bottle initially contains 0.30 litres of water, leaving 1.2 litres of trapped air at a temperature of 17 °C. A pump is used to increase the pressure of the air within the plastic bottle to 2.4 × 10⁵ Pa at the start of lift-off.

Fig. 1.1 shows the rocket at the start of lift-off.

1 litre = 10^–3 m³

Calculate, in moles, the amount of trapped air in the bottle at the start of lift-off.

The trapped air pushes the water downwards out of the hole, causing the rocket to rise. The temperature of this air remains constant.

Calculate the final pressure of the trapped air just before all the water has been released.

Use the data above to show that the upwards force on the rocket at the start of lift-off is about 15 N.

Hence calculate the initial vertical acceleration of the rocket.

initial acceleration =........ m s^–2

Discuss whether adding more water initially would enable the rocket to reach a greater height.