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------------------------------------------------ A 55 kg packing crate is pulled with a constant speed across a rough floor with a rope that is at an angle of 40.8 degrees above horizontal. If the tension in the rope is 145 N, how much work is done to move the crate 4.0 m?

To solve this problem, we first need to find the force acting on the crate in the horizontal direction. This force is equal to the tension in the rope multiplied by the cosine of the angle between the rope and the horizontal:

F_horizontal = Tension * cos(angle) = 145 N * cos(40.8 degrees) = 110.6 N

Next, we can calculate the work done to move the crate using the formula:

Work = Force * Distance * cos(theta)

where theta is the angle between the force and the direction of motion. Since the crate is moving with a constant speed, we know that the net force on it is zero. Therefore, the force of friction acting on the crate must be equal in magnitude to the force we calculated above:

F_friction = F_horizontal = 110.6 N

The angle between the force of friction and the direction of motion is 180 degrees, so we have:

Work = F_friction * Distance * cos(180 degrees) = - 110.6 N * 4.0 m * cos(180 degrees) = - 442.4 J

The negative sign indicates that the work done is in the opposite direction to the displacement of the crate. In other words, the work done by the force of friction is negative because it acts against the motion of the crate. Therefore, the work done to move the crate 4.0 m is -442.4 J.

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