A 15.5 kg mass, slides down a rough inclined plane at an angle of 33.1 to the horizontal, experiencing a frictional force of 6.8 N.Determine the net force acting on the mass.

Question

BlackTom AI · Accepted Answer

Component of gravity along the incline is mg sinθ, so compute that first and then subtract the frictional force (which opposes the motion down the plane).

1) Relevant concepts:
- Weight = mg (m = mass, g = 9.8 m/s^2).
- Component of weight along the incline = mg sin θ.
- Net force down the incline = (mg sin θ) − (frictional force).

2) Step-by-step calculation with intermediate steps:
- m = 15.5 kg, g = 9.8 m/s^2 → mg = 15.5 × 9.8 = 151.9 N.
- θ = 33.1°, sin(33.1°) ≈ 0.5462.
- Component of gravity along plane: mg sin θ = 151.9 × 0.5462 ≈ 82.99 N.
- Frictional force = 6.8 N, opposing motion down the plane.
- Net force down the plane = 82.99 N − 6.8 N = 76.19 N ≈ 76.24 N (rounding to two decimal places).

3) Why this is correct:
The only forces doing work parallel to the plane are the downhill component of gravity (mg sinθ) and friction (opposing motion). Subtracting those yields the resultant (net) force along the incline. The computed net force (~76.2 N) is positive, meaning the block accelerates down the plane.

4) Why the other choices are incorrect:
- a. 120.58 N: This is much larger than the gravitational component along the plane and does not correspond to the correct force balance; it cannot be the net force down the incline.
- c. 127.38 N: This value is essentially mg cosθ (the normal force), not a force parallel to the plane; normal force is perpendicular and does not contribute to net motion down the slope.
- d. 83.04 N: This is approximately mg sinθ (the downhill component of gravity) before subtracting friction; it neglects the 6.8 N frictional force and so is not the net force.

Conclusion: The net force acting on the mass is 76.24 N, matching answer b.

A 15.5 kg mass, slides down a rough inclined plane at an angle of 33.1 to the horizontal, experiencing a frictional force of 6.8 N.Determine the net force acting on the mass.单项选择题

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