A 17.9 kg mass, slides down a rough inclined plane at an angle of 33.7 to the horizontal, experiencing a frictional force of 5.6 N.Determine the acceleration of the mass.

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Consider the scenario: a 17.9 kg mass on a rough incline inclined at 33.7 degrees to the horizontal experiences a frictional force of 5.6 N as it slides downward. To find the acceleration along the plane, we use Newton's second law projected onto the incline.

First, determine the component of gravity pulling the mass down the incline: F_gravity_parallel = m g sin(theta). Here m = 17.9 kg, g ≈ 9.8 m/s^2, and theta = 33.7°. Using sin(33.7°) ≈ 0.554 (roughly between 0.55 and 0.56), we get F_gravity_parallel ≈ 17.9 × 9.8 × 0.554 ≈ 17.9 × 5.434 ≈ 97.2 N.

Second, account for the frictional force opposing the motion: F_friction = 5.6 N. Since the mass slides downward, friction acts upward along the plane, opposing the gravitational component.

Third, compute the net force along the incline: F_net = F_gravity_parallel − F_friction ≈ 97.2 N − 5.6 N ≈ 91.6 N.

Fourth, apply Newton's second law to find acceleration along the plane: a = F_net / m ≈ 91.6 N / 17.9 kg ≈ 5.12 m/s^2.

Putting the numbers together, the acceleration is approximately 5.1 m/s^2 down the incline. Note that if one uses slightly different values for sin(33.7°) or g, the result may shift a bit (e.g., within about ±0.1 m/s^2). The given data also allows for a direct calculation using a = g sin(theta) − (friction / m), which yields the same result within rounding.

In this context, the main sources of variation come from the exact value chosen for sin(33.7°) and the gravitational constant used. Regardless, the friction reduces the gravitational component, yielding a positive acceleration along the plane that is on the order of about 5 m/s^2, not significantly smaller unless friction were notably larger or the angle smaller.

MUF0121 Physics Unit 1 - Semester 2, 2025

A 17.9 kg mass, slides down a rough inclined plane at an angle of 33.7 to the horizontal, experiencing a frictional force of 5.6 N.Determine the acceleration of the mass.

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