A 114 kg boulder slides down a sloping hillside during a landslide. The hillside slopes at an angle of 9.7 degrees to the horizontal, and the frictional forces on the boulder add up to 111.3 N.What is the boulder's acceleration down the slope?

Question

BlackTom AI · Accepted Answer

The component of the weight that drives motion down the slope is mg sinθ, so start with that.

1) Relevant concepts
- Weight = mg (m = 114 kg, g = 9.80 m/s^2).
- Component of weight down an incline = mg sinθ.
- Frictional force opposes motion; net force down the slope = mg sinθ − F_friction.
- Newton’s second law: a = F_net / m.

2) Step-by-step calculation
- Compute weight: m g = 114 kg × 9.80 m/s^2 = 1117.2 N.
- Compute sin(9.7°). Using a calculator: sin(9.7°) ≈ 0.16853.
- Gravity component down slope: mg sinθ = 1117.2 N × 0.16853 ≈ 188.23 N.
- Subtract the frictional force (111.3 N) which acts up the slope: F_net = 188.23 N − 111.3 N = 76.93 N.
- Acceleration: a = F_net / m = 76.93 N / 114 kg ≈ 0.6749 m/s^2.

3) Intermediate steps shown explicitly
- m g = 114 × 9.80 = 1117.2 N
- sin(9.7°) ≈ 0.16853
- mg sinθ = 1117.2 × 0.16853 ≈ 188.23 N
- F_net = 188.23 − 111.3 = 76.93 N
- a = 76.93 / 114 ≈ 0.6749 m/s^2 ≈ 0.68 m/s^2

4) Why this is correct
Friction reduces the downslope driving force; net force divided by mass yields the acceleration. All numbers were applied consistently with SI units.

5) Why other choices are incorrect
- a (8.69 m/s^2) and d (10.85 m/s^2) exceed g and are physically impossible for an object constrained to an incline (and far larger than mg sinθ).
- b (2.63 m/s^2) is larger than the frictionless downslope acceleration g sinθ (~1.65 m/s^2), so it cannot be correct.
- c (0.68 m/s^2) matches the net-force calculation above.

Conclusion: The boulder’s acceleration down the slope is 0.68 m/s^2, which matches the provided correct answer.

A 114 kg boulder slides down a sloping hillside during a landslide. The hillside slopes at an angle of 9.7 degrees to the horizontal, and the frictional forces on the boulder add up to 111.3 N.What is the boulder's acceleration down the slope?数值题

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