A fan creates a steady force of 9 N east on a trolley as it rolls 3.4 m to the east. How much work did the frictional force do on the trolley? Give your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

Because the trolley moves 3.4 m east under a steady 9 N eastward push and does not change speed, the frictional force must be a 9 N westward force. Key concepts: work = force · displacement = F d cos(θ); if kinetic energy does not change (steady speed), the net work is zero so the work by friction equals the negative of the work done by the fan.

1) Relevant knowledge points and concepts
- Definition of work: W = F d cos(θ), where θ is the angle between force and displacement.
- If motion is steady (constant velocity), net force = 0 so the frictional force balances the applied force.
- Opposing force does negative work when displacement is in the opposite direction.

2) Step-by-step reasoning
- Fan force: +9 N east. Displacement: 3.4 m east.
- Friction must be equal in magnitude and opposite in direction: F_f = 9 N west = −9 N (taking east as positive).
- Angle between friction (west) and displacement (east) is 180°, so cos(180°) = −1.

3) Calculations (all intermediate steps)
- W_friction = F_f × d × cos(θ)
- Using magnitude and sign: W_friction = (−9 N) × (3.4 m) = −30.6 J
- Rounded to nearest whole number: −30.6 J → −31 J

4) Why this is correct
- The negative sign shows friction removes kinetic energy (or dissipates the work done by the fan). With steady motion, the fan’s positive work (+30.6 J) is exactly canceled by friction’s negative work (−30.6 J).

5) Why other plausible answers are incorrect
- +31 J would imply friction aids motion, which contradicts friction opposing displacement.
- 0 J would imply no net work by friction, only true if friction were zero (not the case here).
- Larger magnitudes (e.g., −306 J) would come from arithmetic errors (decimal place mistakes).

6) Conclusion
- The frictional force did −30.6 J of work, which rounded to the nearest whole number is −31 J, matching the provided answer (−31).

A fan creates a steady force of 9 N east on a trolley as it rolls 3.4 m to the east. How much work did the frictional force do on the trolley? Give your answer to the nearest whole number.数值题

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