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A student moves a box of books down the hall by pulling on a rope attached to the box. The student applies a force of 185 N at an angle of 25 degrees above the horizontal. The box has a mass of 35 kg, and the coefficient of kinetic friction between the box and the floor is 0.27. Find the acceleration of the box.

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Final answer:

To find the acceleration of the box, we consider the forces acting on it. The student exerts a force of 185 N at an angle of 25 degrees above the horizontal. We use Newton's second law to calculate the acceleration.

Step-by-step explanation:

To find the acceleration of the box, we need to consider the forces acting on it. The student exerts a force of 185 N at an angle of 25 degrees above the horizontal. We can break down this force into its horizontal and vertical components. The vertical component is given by 185 N * sin(25) = 78.6 N. The horizontal component is given by 185 N * cos(25) = 167.4 N.

The weight of the box is given by the mass times the acceleration due to gravity, which is 35 kg * 9.8 m/s^2 = 343 N.

The force of friction is given by the coefficient of kinetic friction multiplied by the normal force, which is the weight of the box. So the force of friction is 0.27 * 343 N = 92.61 N.

Since the box is moving, the net force in the horizontal direction is given by the applied force minus the force of friction. So the net force in the horizontal direction is 167.4 N - 92.61 N = 74.79 N.

Using Newton's second law, F = ma, we can calculate the acceleration of the box. So the acceleration of the box is 74.79 N / 35 kg = 2.14 m/s^2.

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