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Calculate the magnitude of the normal force on a 10.2 kg block in the following circumstances. (Enter your answer in N.)

The block is on a level surface, and a force of 115 N is exerted on it at an angle of 40.8° above the horizontal.

Answer :

Final answer:

The magnitude of the normal force on a 10.2 kg block with a 115 N force applied at a 40.8° angle is approximately 25.44 N, calculated by considering the gravitational force and the vertical component of the applied force.

Explanation:

Calculating the Normal Force

To calculate the normal force on a 10.2 kg block, we need to consider the gravitational force acting on it as well as the vertical component of the applied force. On a flat surface, the normal force N is equal to the gravitational force mg if there is no vertical component of any other force. However, with an applied force at an angle, part of this force counteracts gravity, altering the normal force.

First, compute the gravitational force (weight):
W = mg = 10.2 kg × 9.8 m/s2 = 99.96 N.

Second, calculate the vertical component of the applied force: Fy = F × sin(θ) = 115 N × sin(40.8°) = 74.52 N.

Finally, to find the normal force, subtract Fy from W: N = W - Fy = 99.96 N - 74.52 N = 25.44 N.

Therefore, the magnitude of the normal force on the block is approximately 25.44 N.

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