Gravity & weight

The photograph shows a lever-arm balance. The balance can be used to measure the mass of objects to the nearest gram.

The lever-arm is a length of metal, bent at one end as shown in the diagram below. The lever-arm can rotate around the pivot, P.

The arrangement is in equilibrium.

State the two conditions needed for the arrangement to be in equilibrium.

Determine the weight of the counterweight.

Assume the mass of the lever-arm is negligible.

mass of pan = 260 g

An object is placed in the pan. The lever-arm moves along the scale.

Explain why the lever-arm pointer moves through a large distance whilst the pan moves a much shorter distance.

Helium is available in small metal canisters. The helium can be used to fill party balloons.

A full canister contains helium gas at a temperature of 18.5C and a pressure of 1.65×10⁷Pa. The canister is approximately spherical, with a radius of 4.3610^–2m.

Calculate the mass of helium gas in the full canister.

mass of 6.02×10²³ atoms of helium = 4.00×10^–3kg

Student X and Student Y discuss the weight of the canister and its contents after a number of balloons have been filled.

Student X suggests that the weight will have increased, because the upthrust exerted on the canister by the helium will be reduced.

Student Y suggests that the weight will have decreased, because helium has been released from the canister.

Assess which student’s suggestion is correct.

A student investigated the behaviour of small, positively charged oil drops in an electric field.

He introduced an oil drop between two horizontal metal plates. A potential difference V was applied to bring the oil drop to rest as shown.

Add to the diagram to show the polarity of the power supply when the oil drop is at rest.

The oil drop was at rest when V = 4870 V.

The student expected the charge on the oil drop to be a whole number multiple of the charge on an electron.

Deduce whether this is confirmed by the experimental data.

distance between top plate and bottom plate = 1.55 cm

The student determined the terminal velocity of the oil drop in order to obtain a value for the weight of the oil drop.

He disconnected the power supply and the oil drop fell downwards. He viewed the oil drop through a microscope.

Explain why the student should wait a short while before starting to take measurements.

The view through the microscope is shown below. The scale is in millimetres.

The position of the oil drop at the start and end of a 120 s time interval is indicated by the black dots.

Determine the terminal velocity of the oil drop.

The student repeated the measurements on fifty oil drops. For each drop the student calculated the charge on the oil drop.

His results are shown in the bar chart.

The student predicted that the charge on each oil drop would be a whole number multiple of the charge on an electron.

Comment on the extent to which the bar chart supports the student’s prediction.

The International Space Station (ISS) orbits the Earth with a constant speed v. The orbit is circular and of radius r.

The diagram represents two positions, A and B, of ISS during its orbit.

Draw a labelled vector diagram, in the space below, of the velocities at the two positions that shows the acceleration is directed towards the centre of the orbit.

The ISS completes one orbit in 92 minutes.

Calculate the centripetal acceleration of the ISS.

r = 6800 km

Astronauts in the ISS are often described as being “weightless”.

Discuss whether the astronauts are “weightless” when they are orbiting the Earth in the ISS.

The length l of wire in the magnetic field was 15.5 cm. When the current in the circuit was 4.55 A, the reading on the balance increased by 5.65 g.

Calculate the magnetic flux density B in the region of the rigid wire.

The student wrote the following statement

“The balance could read to the nearest 0.01 g, which makes my values for the magnetic force both accurate and precise.”

Comment on this statement.

A uniform paving slab is to be used as a garden step.

State what is meant by the centre of gravity of an extended body.

The paving slab has a weight of 310 N and a length of 90 cm and will be supported at two points, P and Q, as shown. The distance between P and Q will be 75 cm.

This might be unsafe because a person who places all their weight at the end of the slab might tip the slab.

A person of mass 70 kg stands at the end of the slab.

Deduce whether the slab will tip.