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Energy Conservation on a Frictionless Track: Public Worked Question

A public energy-conservation question showing why mass cancels when gravitational potential energy converts into speed on a frictionless track.

Question

A 2.0 kg2.0\,\text{kg} block is released from rest at the top of a frictionless track and slides down through a vertical drop of 5.0 m5.0\,\text{m}. Taking g=10 m/s2g = 10\,\text{m/s}^2, what is the block's speed at the bottom?

  1. a.7.1 m/s7.1\,\text{m/s}
  2. b.10 m/s10\,\text{m/s}
  3. c.50 m/s50\,\text{m/s}
  4. d.100 m/s100\,\text{m/s}

Correct answer

B. 10 m/s10\,\text{m/s}

Full reasoning

  1. 1Only gravity does work on the frictionless track, so mechanical energy is conserved: mgh=12mv2mgh = \tfrac{1}{2}mv^2.
  2. 2The mass cancels from both sides, so the 2.0 kg2.0\,\text{kg} value never enters the answer.
  3. 3Solve for the speed: v=2gh=2(10)(5.0)=100v = \sqrt{2gh} = \sqrt{2(10)(5.0)} = \sqrt{100}.
  4. 4The block reaches the bottom at 10 m/s10\,\text{m/s}, so choice B is correct.

Why each choice is right or wrong

Choice A

This is gh\sqrt{gh}; the factor of 2 that appears when solving 12mv2=mgh\tfrac{1}{2}mv^2 = mgh was dropped.

Choice B

Correct. v=2gh=2(10)(5.0)=100=10 m/sv = \sqrt{2gh} = \sqrt{2(10)(5.0)} = \sqrt{100} = 10\,\text{m/s}, independent of the mass.

Choice C

This equates mghmgh to mv2mv^2 (dropping the one-half) and then never takes the square root, reporting ghgh itself.

Choice D

This is v2=2ghv^2 = 2gh reported as a speed; the final square root was skipped entirely.

Related formula

Energy conservation for a gravity-only drop

mgh=12mv2mgh = \tfrac{1}{2}mv^2

Assumptions: Friction and air resistance are negligible. The object starts from rest.

Related topic and practice

Energy and Momentum ConservationSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 1, Section 8.3: Conservation of Energy — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
Publisher record
Keiko Study editorial owner
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Reviewer record
Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

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