Scalar & vector quantities

Which of the following is a scalar quantity?

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.

An electrical conductor XY carries a current I as shown.

The current density j is defined as j = where A is the cross‑sectional area of the conductor.

Current density is a vector quantity.

State what is meant by a vector quantity.

I is constant but A decreases towards end Y.

Explain how this affects the drift velocity of the free electrons in the conductor.

The resistivity ρ of the conducting material is given by ρ = where E is the electric field strength.

Show that the units are the same on both sides of this equation.

Which of the following quantities is a vector?

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

A ‘tennis trainer’ consists of a tennis ball suspended by a string from the top of a vertical pole. When the ball is hit it travels in a horizontal circle around the pole, as shown in both the photograph and the diagram.

The radius of the path of the ball is 1.2 m and the speed of the ball is 3.8 m s⁻¹.

Deduce whether these values are consistent with the angle between the string and the vertical pole shown in the photograph.

Which of the following is an example of a scalar quantity?

Which of the following is an example of a scalar quantity?

Scientists have been studying a type of jumping spider that can jump up to six times its body length.

The scientists photographed a spider at 0.02s intervals, during a jump. The picture is taken from the photograph and is shown actual size.

Deduce whether the images show that the motion in the x-direction is independent of the motion in the y-direction. You should take measurements using the cross marking the centre of gravity of the spider.

Show that the initial velocity of the spider at the start of the jump is about 1 m s⁻¹. You should take measurements using the cross marking the centre of gravity of the spider.

The spider achieves this jump by extending its two back legs by 3.0 mm.

Calculate the average force the spider exerts in each leg to achieve the jump.

mass of spider = 150 mg

Just as the spider starts the jump, it fixes a silk thread to the platform. It is thought that the thread acts as a safety line in case the spider falls.

A student makes the comment:

ʻIf the silk thread can withstand a tension equal to the weight of the spider then this safety system should work.ʼ

Deduce whether this statement is correct.

The shot put is an Olympic field event. The distance for the women’s world record shot put is in excess of twenty two metres.

The shot is a metal ball, which is thrown from a standing position so that it lands on the ground a horizontal distance R away from the thrower.

A shot is thrown from a height h above the ground with an initial velocity of 14.2 m s^–1 at an angle of 37.0° to the horizontal. The time it takes for the shot to reach the ground is 1.98 s.

Show that the vertical component of the initial velocity is about 8.6 m s^–1.

Calculate the height h above the ground from which the shot was thrown.

Calculate the horizontal distance R for this throw.

A student investigates the motion of a friction‑free trolley down a ramp. On the top of the trolley there is a metal loop which makes contact with a length of thin resistance wire, AB, fixed above the ramp. The resistance wire has a uniform diameter.

The trolley accelerates down the ramp and the metal loop stays in contact with the wire along the full length of the ramp.

The student uses a protractor to measure the angle θ between the ramp and the horizontal

and records a value of 4° with an uncertainty of ±1°.

The two ends of the wire are connected to a 1.5 V cell. A data logger, set to measure potential difference, is connected to the metal loop and to the negative terminal of the cell.

Explain how the potential difference recorded by the data logger will vary as the loop moves along the length of the wire AB.

The graph shows the data obtained from the data logger.

Determine the velocity of the trolley at 1.5 s.

1.5 V represents a distance of 2.00 m.

The student calculated the velocity of the trolley at 2.0 s to be 1.5 m s^–1.

By considering the acceleration of the trolley, determine whether the student’s measurement of θ was within the uncertainty quoted.