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A 16.9 kg block is dragged over a rough, horizontal surface by a constant force of 93.9 n acting at an angle of 31.8° above the horizontal. The block is displaced 97.1 m, and the coefficient of kinetic friction is 0.105. Find the work done by the 93.9 N force. The acceleration of gravity is 9.8 m/s? answer in units of j.

a) 7786.97 J
b) 6540.23 J
c) 8263.18 J
d) 7129.84 J

User Tgkokk
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Final answer:

To find the work done by the 93.9 N force, calculate the force component in the direction of displacement and the work done against friction. The work done by the force is 4964.5048 J and the work done against friction is 1441.142 N. The total work done is 6405.6468 J.

Step-by-step explanation:

To find the work done by the 93.9 N force, we need to calculate the force component in the direction of displacement. We can do this by finding the vertical and horizontal components of the force. The vertical component can be found by multiplying the force by the sine of the angle: 93.9 N * sin(31.8°) = 51.1488 N. The horizontal component can be found by multiplying the force by the cosine of the angle: 93.9 N * cos(31.8°) = 80.2476 N.

Next, we need to calculate the work done against friction. The frictional force can be found by multiplying the coefficient of kinetic friction by the normal force. The normal force can be found by multiplying the weight of the block by the cosine of the angle. The weight of the block can be found by multiplying the mass of the block by the acceleration due to gravity: 16.9 kg * 9.8 m/s² = 165.82 N. The normal force is then 165.82 N * cos(31.8°) = 141.5975 N. The frictional force is 0.105 * 141.5975 N = 14.8676 N.

The work done by the 93.9 N force is equal to the force component in the direction of displacement multiplied by the displacement: 51.1488 N * 97.1 m = 4964.5048 J. The work done against friction is equal to the frictional force multiplied by the displacement: 14.8676 N * 97.1 m = 1441.142 N.

The total work done is the sum of the work done by the force and the work done against friction: 4964.5048 J + 1441.142 N = 6405.6468 J.

User Eugene Yu
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