IB Physics HL A.3 practice question

Question 1

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.