IB Physics HL Theme A: Space, time and motion questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

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Question 1

Multiple choiceHard1 mark

A body of mass $M$ moves at speed $u$ along the $+x$ -direction and explodes into two pieces of masses $\alpha M$ and $(1-\alpha)M$ where $0<\alpha<1$ The piece of mass $\alpha M$ moves at speed $v$ perpendicular to the original motion. The external impulse during the explosion is negligible. What is the speed of the other piece divided by $u$

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Answer: C. Total momentum is conserved as a vector. The other piece must have momentum components $Mu$ and $-\alpha Mv$ so its speed is

\frac{\sqrt{(Mu)^2+(\alpha Mv)^2}}{(1-\alpha)M}.

Dividing by $u$ gives $\dfrac{\sqrt{1+\alpha^2(v/u)^2}}{1-\alpha}$

A: assigns mass $\alpha M$ rather than $(1-\alpha)M$ to the other piece.
B: adds the perpendicular momentum components as scalar magnitudes.
D: uses only the $x$ -component and omits the momentum needed to cancel the first piece’s perpendicular component.
Remember: conserve momentum in each perpendicular direction before finding a resultant speed.

Question 2

Multiple choiceHard1 mark

An electric winch raises a 40 kg load 6.0 m up a ramp at constant speed. The rope exerts a constant 250 N force parallel to the load’s 12 m displacement. The winch receives 4.0 kJ of electrical energy. Take $g=10\ \mathrm{N\,kg^{-1}}$ and assume all energy not retained as gravitational potential energy is transferred to thermal stores.

I. The work done by the rope on the load is 3.0 kJ.
II. A Sankey diagram for the winch and load together shows 2.4 kJ of useful gravitational potential energy output and 1.6 kJ of thermal output.
III. The work done by the rope on the load equals the load’s increase in gravitational potential energy.

Which statements are correct?

Show answer and explanation

Answer: C. The rope’s work is $W=Fs=(250)(12)=3.0\times10^3\ \mathrm{J}$ so I is true. The increase in gravitational potential energy is $mg\Delta h=(40)(10)(6.0)=2.4\times10^3\ \mathrm{J}$ For the winch and load together, the remaining $4.0-2.4=1.6\ \mathrm{kJ}$ is transferred to thermal stores, so II is true; not all the rope’s work is retained as gravitational potential energy, making III false.

A: Uses the vertical rise rather than the displacement parallel to the rope force to evaluate the work in I.
B: Treats all $3.0\ \mathrm{kJ}$ of rope work as useful gravitational potential energy, leaving only $1.0\ \mathrm{kJ}$ as thermal output.
D: Equates the rope’s energy transfer with the energy retained as gravitational potential energy, overlooking the thermal transfer.

Remember: work is energy transferred by a force; it need not all be retained in one energy store.

Question 3

Multiple choiceEasy1 mark

A train moves at constant velocity to the right relative to a platform. Light flashes are emitted from its front and rear, and a passenger at the train’s midpoint receives them simultaneously. Which row gives the emission times of the flashes in the train and platform frames?

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Answer: A. The passenger is equally distant from both ends in the train frame, so simultaneous arrival means the emissions were simultaneous in that frame. Relativity of simultaneity means they are not simultaneous in the platform frame; for a train moving right, the front emission is later.

B: reverses the event order in the platform frame; the front emission is later, not the rear one.
C: treats simultaneity as unchanged between frames and assigns the front event an earlier time in the train frame.
D: also assigns simultaneity to the platform frame, and reverses the front–rear order in the train frame.
Remember: events simultaneous in one inertial frame need not be simultaneous in another.

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