A golf ball receives an impulse of 3.9 Ns when it is in contact with a golf club for 6.1 milliseconds. What force did the club exert on the ball? Give your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

Impulse equals average force multiplied by the contact time, so F = impulse / Δt.

1) Relevant concepts:
- Impulse J (in N·s) equals the change in momentum and also equals the average force times the contact time: J = F·Δt.
- Units must be consistent: milliseconds must be converted to seconds before using the formula.

2) Step-by-step reasoning and intermediate steps:
- Given impulse J = 3.9 N·s.
- Contact time Δt = 6.1 milliseconds = 6.1 × 10^−3 s = 0.0061 s.
- Solve for average force: F = J / Δt.

3) Calculation with intermediate values:
- F = 3.9 N·s ÷ 0.0061 s
- To simplify, multiply numerator and denominator by 1000: F = 3900 ÷ 6.1
- 3900 ÷ 6.1 = 639.3442623... N

4) Why this answer is correct:
- The impulse formula directly relates the known impulse to the average force over the known contact time. Using consistent SI units produces an average force of about 639.344 N. Rounding to the nearest whole number gives 639 N.

5) Common incorrect approaches (why they’re wrong):
- Forgetting to convert milliseconds to seconds (using 6.1 instead of 0.0061) would give 3.9/6.1 ≈ 0.639 N, which is incorrect by three orders of magnitude.
- Using an unrelated formula (for example F = ma without knowing mass or acceleration) does not apply here because impulse is given directly.

6) Conclusion:
- Therefore the average force exerted by the club is approximately 639 N, which matches the provided correct answer.

A golf ball receives an impulse of 3.9 Ns when it is in contact with a golf club for 6.1 milliseconds. What force did the club exert on the ball? Give your answer to the nearest whole number.数值题

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