Power

The diagram shows a section through the components of a speedometer for a bicycle. The front wheel axle of the bicycle is connected to a cable. The cable rotates as the bicycle wheel rotates. The other end of the cable is connected to a magnet which also rotates, as shown.

An aluminium disc is shaped so that it is close to, but not touching, the magnet. The disc is connected to a pointer by a shaft. A spring prevents the disc and shaft from freely rotating.

*(a) Explain why the aluminium disc rotates in the same direction as the magnet.

The road speed of the bicycle should be displayed by the speedometer.

Explain why the displayed speed can not be accurate, as bicycles can have different wheel diameters.

The potential difference (p.d.) from a power pack alternates at a frequency of 50 Hz. The root-mean-square (r.m.s.) value of the output p.d. is measured to be 8.5 V using an a.c. voltmeter.

The output from the power pack is connected to a resistor of resistance 1.5 Ω.

Show that the rate of power dissipation in the resistor is about 48 W.

A lab technician used the resistor to heat 1.25 10^–4m³ of milk in a beaker.

Calculate the time taken for the milk to increase in temperature by 12 °C.

specific heat capacity of milk = 3930 J kg^–1K^–1

The lab technician used an oscilloscope to determine the supply frequency and check the r.m.s. output p.d. displayed by the voltmeter.

Describe the methods the technician should use.

A toy car moves up a slope at a constant speed, as shown. The car is moved by a motor with a power output of 5.2 W. The car gains a gravitational potential energy of 0.40 J in a time of 1.1 s.

Which of the following expressions gives the work done, in J, against resistive forces?

Electric vehicles use a direct current (d.c.) electric motor powered by a battery for propulsion. A simplified diagram of a d.c. electric motor is shown.

A split ring consists of two semi‑circular sections that are attached to a coil. The coil is labelled ABCD. Two brushes, made of carbon, rub against and make electrical contact with the split ring.

*(a) Describe how this arrangement can lead to the coil rotating.

An advert for an electric car has the following information:

• electric motor can develop up to 390 kW output power

• car achieves a velocity of 28 m s^–1 from rest in 4.0 s at maximum power

Calculate the work done by resistive forces when the car accelerates to a velocity of

mass of car = 1950 kg

A website suggests that ‘fast‑charging’ the battery in an electric vehicle can increase the internal resistance of the battery.

Explain why an increase in internal resistance of a battery is a disadvantage.

A student drives a go‑kart up a slope.

The slope is at an angle of 5.7° to the horizontal. The go‑kart moves with a constant

Calculate the power of the go‑kart.

mass of go‑kart and driver = 60 kg resistive force on the go‑kart = 18 N

The go‑kart is powered by a battery connected to a motor. The rate of thermal energy transfer by the wiring in the motor is 55 W.

Calculate the resistance of the wiring in the motor.

current in motor = 24 A

The world solar challenge is set every two years, in Australia. The challenge is to complete a three thousand kilometre route with a vehicle powered only by the Sun.

Vehicles have their surfaces fitted with solar panels, as shown in the photograph.

(Source: © LAURENT DOUEK/LOOK AT SCIENCES/SCIENCE PHOTO LIBRARY)

One of the solar panels has an e.m.f. of 8.2 V when in sunlight. The terminal potential difference is 5.5 V when a current of 0.45 A is drawn from the solar panel.

Calculate the internal resistance of the solar panel in these conditions.

A bank of 380 of these solar panels is used to charge the battery in a vehicle. The panels are connected in parallel and the current provided by each panel is 0.45 A. When fully charged, the energy stored in the battery is 12 kW h.

Calculate the time, in hours, to fully charge this battery if the solar panels are in sunlight. Assume the efficiency of charging this battery is 100%.

The vehicle can reach a maximum speed of 34 m s⁻¹ on flat ground. The electric motor used to move the vehicle has a power of 4.5 kW.

Calculate the initial acceleration of the vehicle as it starts from rest.

mass of vehicle and driver = 420 kg

State one assumption made in this calculation.

Solar power alone would not be suitable for a family car because it is not sunny all the time.

Give two further reasons why solar power alone would not be suitable.

The apparatus shown can be used to determine a value for the specific latent heat of vaporisation of water.

In one experiment the current in the heater was 8.20 A, and the potential difference across the heater was 230 V.

Show that the power of the heater was about 2 kW.

There was 0.655 kg of water in the flask at an initial temperature of 22.5 °C. The heater was switched on, and the water in the flask was heated to boiling point.

Calculate the minimum time taken for the water to be heated to 100.0 °C.

specific heat capacity of water = 4190 J kg⁻¹K⁻¹

The heater was left on and water continued to boil in the flask. The water was allowed to boil for a few minutes. The conical flask was then placed under the heat exchanger and water was collected in it.

Give a reason why the water was left boiling for a few minutes before the conical flask was put in place.

Water with a mass of 95.0 g was collected in a time of 125 s.

Calculate the rate of energy transfer in the heat exchanger.

specific latent heat of vaporisation of water = 2.26 × 10⁶J kg⁻¹

Discuss your answers to (a)(i) and (b)(ii).

State how the apparatus could be modified to minimise the effect of a significant source of error.

In the sport of curling, two teams of ‘curlers’ take turns sliding polished granite stones across an ice surface towards a circular target marked on the ice.

A stone of mass 19.6 kg is accelerated uniformly for 1.25 s before being released by a curler. The stone then decelerates uniformly to rest, travelling 32.5 m in a time of 17.5 s.

Calculate the average useful power developed by the curler in accelerating the stone.

*(b) Stone B is stationary. Stone A travels towards the target and makes a direct hit on stone B as shown. Both stones have mass m.

The collision is elastic. Just before the collision stone A has a velocity v. After the collision stone B moves off with velocity v.

Discuss how the relevant conservation laws apply to this collision.

While a stone is moving towards the target, the curlers vigorously sweep the ice directly in front of the stone.

Explain why this may make the stone travel further.

Motors usually have a rotating component which can do work W.

In the diagram below, electric field lines have been drawn around one pair of these spheres.

Add to the diagram to show • the directions of the field lines • the lines of equipotential.

The distance between the centres of each charged sphere in this pair is 5.0 cm.

Show that the force between this pair of charged spheres is about 0.04 N.

charge on each sphere = 0.10 μC

The table shows the typical power and the corresponding angular velocity required for three different appliances.

Deduce which of these appliances, in principle, could use the electrostatic motor in (b).

You should use the word equation in (a) and assume that the length of the rod in the electrostatic motor is 8.0 cm.

Assume that the electrostatic motor would deliver a constant force throughout one complete rotation.