Physical quantities and units

Explain why the Young modulus and the breaking stress of a wire have the same SI unit.

Table 1 contains data about four metal wires W, X, Y and Z.

The metal used to make wire X costs £75 per gram.

Calculate, in £, the cost of wire X.

State and explain which of the wires in Table 1 are made from the same material.

One of the wires in Table 1 was used to obtain the stress–strain data shown in Figure 5.

Draw a line of best fit on Figure 5. Go on to deduce, using your line of best fit and Table 1, whether wire W could have been used to produce Figure 5.

A force F moves through a distance x in the direction of F.

In which row is the work done by the force 1 J ?

Figure 5 shows apparatus to investigate how the resistance R of a lamp filament varies with the absolute temperature T of the filament.

The lamp is inside an oven.

The oven temperature is increased to a steady value. The filament is at the same temperature as the inside of the oven.

The temperature T in kelvin is determined using the thermometer. An ohm-meter is connected to the filament to determine R at temperature T.

The oven temperature is increased to new steady values and further readings of T and R are recorded.

Figure 6 shows the variation of R with T.

It can be shown that:

where:

R₀ is the resistance of the filament at temperature T₀ α is a constant.

Determine α using the graph in Figure 6. State an appropriate SI unit for your answer.

In a different investigation, a student investigates how the electrical power P transferred in the same filament lamp varies for values of T greater than 800 K.

The student assumes that α is constant for all values of T.

Figure 7 shows the circuit that the student uses. The temperature of the filament is controlled by the energy supplied to it from the battery.

Complete Table 2.

It can be shown that P₁ Tⁿ where n is an integer.

Determine n.

In your answer you should:

• use Table 3 to organise the data you will plot

• plot a suitable graph on Figure 9.

A laser emits light of wavelength 600 nm for 10 ns.

What is the number of complete waves emitted by the laser?

This question is about a method to investigate how the force on a conductor varies with flux density and current (required practical activity 10).

Figure 10 shows a copper rod clamped above a horizontal bench.

Figure 10

Describe a method to show that the copper rod is horizontal. Your method must include the use of a metre ruler. You may annotate Figure 10.

Figure 11 shows the copper rod positioned above a digital balance.

Two identical magnets are mounted on a steel yoke with their opposite poles facing each other. The balance is zeroed. The yoke is then placed on the balance so that a horizontal uniform magnetic field is applied perpendicular to the copper rod. The ends of the rod are connected as shown.

When the switch is open, the reading on the balance shows the mass of the yoke and the two magnets. When the switch is closed, the reading on the balance decreases.

Explain, with reference to Figure 11, the direction of the horizontal magnetic field.

The current I in the rod is varied. The balance reading M₁ is recorded for different values of I.

The switch is now opened. Two additional magnets, identical to those used before, are attached to the yoke.

Figure 12 shows how this new arrangement compares with the arrangement in Figure 11.

The balance reading with four magnets attached to the yoke is M₂. With the switch open, M₂ is the mass of the yoke and the four magnets.

The switch is now closed. M₂ is recorded for different values of I.

Figure 13 shows data from both experiments. Values of M₁ and M₂ are plotted using different vertical axes.

It can be shown that

M = kBI + nZ + Y

where

M = balance reading when the current is I B = magnetic flux density of the horizontal uniform magnetic field n = number of magnets attached to the yoke Z = mass, in g, of each magnet Y = mass, in g, of the yoke k is a constant.

Deduce the fundamental base units for k.

Determine Y.

A student sets up the apparatus with the copper rod positioned incorrectly.

Figure 14 shows how the student’s arrangement compares with the correct arrangement.

The student produces a graph of M₁ against I.

Compare the student’s graph with the graph of M₁ against I (the solid line) in Figure 13. Explain your answer.

Which two quantities have the base unit kg m² s⁻²?

Which gives SI prefixes in descending order of magnitude?

Which is approximately equal to 3 kW h ?

Which is the shortest distance?

constant.

What is a possible SI unit for k ?

What quantity is measured in kW h ?

Safety barriers are used on UK motorways to prevent vehicles crossing from one carriageway to the other carriageway. The barriers also absorb some of the kinetic energy of a vehicle and deflect vehicles along the barrier.

The standard test of a safety barrier uses a vehicle that contains dummies. The total mass of the vehicle and its contents is 1.5 × 10³ kg and its initial speed is 110 km h^–1

Show that the initial kinetic energy of the test vehicle is 700 kJ.

The test vehicle hits a steel safety barrier at an angle of 20°, as shown in Figure 7.

Calculate the component of the momentum of the test vehicle in a direction along the line of the safety barrier. Give an appropriate unit for your answer.

Immediately after the collision, the test vehicle moves along the safety barrier with no change in its momentum in this direction.

Show that the kinetic energy lost in the collision is about 80 kJ.

The steel safety barrier deforms during the collision. For the barrier to pass the test, the test vehicle should not move more than 1.5 m towards the other carriageway.

The barrier can apply an average force of 60 kN at right angles to the carriageway.

Deduce whether the safety barrier will pass the test.

A different safety barrier uses a solid concrete wall which does not deform. The same standard test is carried out on a concrete wall.

Discuss which type of barrier would cause less damage to the dummies in the test.

A load of 50 N is suspended from a wire that has an area of cross-section of 1 mm².

The stress in the wire, in Pa, is between

What is a correct unit for the area under a force − time graph?