a) The work done (W) can be expressed as the dot product of the force (F) and the displacement (d):
W = F * d * cos(theta)
Where theta is the angle between the force and the displacement. In this case, since the box is being pulled horizontally, the angle theta is 0 degrees, so cos(theta) = 1.
Given that the work done is 250 J and the displacement is 12 m, we can rearrange the equation to solve for the force:
F = W / (d * cos(theta))
F = 250 J / (12 m * 1)
F = 250 J / 12 m
F ≈ 20.83 N
b) Since the box is moving at a constant velocity, the net force acting on it is zero. This means that the force of friction must be equal and opposite to the force of tension in the rope.
Therefore, the force of friction is also approximately 20.83 N.
To calculate the work done by the force of friction, we use the equation:
Work = Force * displacement * cos(theta)
Since the force of friction is opposing the displacement of the box, the angle theta between the force and the displacement is 180 degrees, so cos(theta) = -1.
Work = -20.83 N * 12 m * -1
Work = 250 J
Therefore, the work done by the force of friction is 250 J.
A horizontal rope is used to pull a box forward across a rough floor doing 250 J of work over a
horizontal displacement of 12 m at a constant velocity.
a) Calculate the force of tension in the rope.
b) Calculate the force of friction and the work done by the force of friction.
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