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 $u$

Show answer and explanation

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.

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