Physics Work & Energy UHS 2023
PMDC Verified Question 23 of 108
An 8.0 kg box slides along a horizontal frictionless floor at 3 m/s and collides with a relatively massless spring that compresses 12 cm before the box comes to a rest. Calculate the retarding force of the spring.
A
3 N
B
30 N
C
300 N
D
3000 N
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 300 N
Concept:

By the Work-Energy theorem, the work done by the retarding force (average force) equals the total kinetic energy removed from the box.

Formula:

$$ W = F_{\text{avg}} \times x = \Delta K.E = \frac{1}{2}mv^2 $$

Solution:

  • Mass (\( m \)) = 8.0 kg, Velocity (\( v \)) = 3 m/s.


  • Compression distance (\( x \)) = 12 cm = 0.12 m.


  • Initial \( K.E = \frac{1}{2}(8)(3)^2 = 4 \times 9 = 36 \text{ J} \).


  • The spring absorbs this 36 J doing work: \( F \times 0.12 = 36 \).


  • \( F = \frac{36}{0.12} = \frac{3600}{12} = 300 \text{ N} \).


Why other options are incorrect:

Failing to convert 12 cm to meters yields 3 N (Option A). Simple arithmetic errors with decimal places yield 30 N or 3000 N.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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