DP Physics Questionbank

In the reference frame of the laboratory the force on X is magnetic.

(i) State the nature of the force acting on X in this reference frame where X is at rest.

(ii) Explain how this force arises.

State what is meant by a reference frame.

State and explain whether the force experienced by P is magnetic, electric or both, in reference frame S.

State and explain whether the force experienced by P is magnetic, electric or both, in the rest frame of P.

State one prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.

A current is established in a long straight wire that is at rest in a laboratory.

A proton is at rest relative to the laboratory and the wire.

Observer X is at rest in the laboratory. Observer Y moves to the right with constant speed relative to the laboratory. Compare and contrast how observer X and observer Y account for any non-gravitational forces on the proton.

State whether the field around the wire according to observer X is electric, magnetic or a combination of both.

Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.

Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.

Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.

Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.

explain why the time coordinate of E in frame S is $t=\frac{L}{c}$.

hence show that the space coordinate of E in frame S is $x=L+\frac{vL}{c}$.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.

Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.

Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.

Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.

Explain how the force in part (b)(ii) arises.

A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96c relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.

State which of the two time intervals is a proper time.

Calculate the speed v of the train for the ratio $\frac{\mathrm{\Delta }{t}_{\text{P}}}{\mathrm{\Delta }{t}_{\text{Q}}}=0.30$.

Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to be 125 m. The train enters a tunnel of length 100 m according to observer Q.

Show that the length of the train according to observer Q is 100 m.

Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is 2.5 × 10^–7 s.

Demonstrate that the spacetime interval between events B and F is invariant.

A second train is moving at a velocity of –0.70c with respect to the ground.

Calculate the speed of the second train relative to observer P.

Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above ground and move downwards at a speed of 0.98c relative to the ground. For this speed $\gamma$ = 5.0. Discuss, with suitable calculations, how this experiment provides evidence for time dilation.

Calculate the length of the rocket according to X.

A space shuttle is released from the rocket. The shuttle moves with speed 0.20c to the right according to X. Calculate the velocity of the shuttle relative to the rocket.

the time interval between the lamps turning on.

which lamp turns on first.

Calculate the value of c ²t ² – x ².

Identify the terms in the formula.

u′ = $\frac{u-v}{1-\frac{uv}{c^2}}$

Determine, according to an observer in A, the velocity of B.

Determine, according to an observer in A, the time taken for B to meet A.

Discuss the change in d according to observer Y.

Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.

Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.

Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.

Calculate the velocity of rocket B relative to rocket A.

Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.

Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.

Calculate the velocity of the spaceship relative to the Earth.

The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.

As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.

Explain what is meant by the statement that the spacetime interval is an invariant quantity.

calculate the spacetime interval.

determine the time between them according to observer B.

Outline why the observed times are different for A and B.

Calculate the speed of the probe relative to the ground.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.

x′ = 1.5 m.

ct′ = –1.1 m.

Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.

Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).

Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².

Explain how the force in part (b)(ii) arises.

The velocity of P is 0.30c relative to the laboratory. A second particle Q moves at a velocity of 0.80c relative to the laboratory.

Calculate the speed of Q relative to P.

Calculate, for observer A, the length L_A of the bridge

Calculate, for observer A, the time taken to cross the bridge.

Determine the time, according to observer A, between X and Y.

Deduce the length of the probe as measured by an observer in the spaceship.

Explain which of the lengths is the proper length.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the speed of the probe in terms of $c$, relative to Earth.

Calculate the angle between the worldline of S and the worldline of the Earth.

Determine the time taken for the journey in the reference frame of twin B.

Draw the time $c{t}^{\prime }$ and space $x^{\prime }$ axes for observer P’s reference frame on the spacetime diagram.

Deduce, using the spacetime diagram, which light was turned on first according to observer P.

On the diagram label the coordinates x and ct.

State and explain whether the ct coordinate in (c)(i) is less than, equal to or greater than 1.0 m.

For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).

Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.

Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.

Construct event A and event B on the spacetime diagram.

Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.

Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.

Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.

Label, with the letter E, the event of the spaceship going past the planet.

Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.

Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.

Determine, using the diagram, the speed of the spacecraft relative to the galaxy.

Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$'.

Calculate in terms of $c$ the velocity of spaceship A relative to observer O.

Draw the $x\text{'}$ axis for the reference frame of spaceship A.

Plot the event E on the spacetime diagram and label it E.

Determine the time, according to spaceship A, when light from event E was observed on spaceship A.