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Explain Bot To determine the weight of the cylinder, we can use the concept of equilibrium. In this problem, the minimum force required to hold the cylinder from slipping against the belt and the wall is given as P = 60 lb. We need to find the weight of the cylinder, which is represented by the force of gravity acting on it.
First, let's analyze the forces acting on the cylinder. We have the force of gravity acting downwards, the normal force exerted by the belt and the wall acting upwards, and the friction force acting in the horizontal direction.
Since slipping does not occur at the wall, we can assume that there is no friction force acting between the cylinder and the wall. Therefore, the only friction force acting on the cylinder is between the belt and the cylinder.
The friction force (Ff) can be calculated using the formula:
Ff = μs * N
where μs is the coefficient of friction between the belt and the cylinder and N is the normal force.
In equilibrium, the sum of the forces in the vertical direction should be zero. Therefore, the normal force N is equal to the weight of the cylinder (W).
Now, we can substitute the values into the equation:
Ff = μs * W
Given that μs = 0.3 and P = 60 lb, we can solve for the weight of the cylinder:
60 lb = 0.3 * W
Dividing both sides of the equation by 0.3, we get:
W = 60 lb / 0.3
W ≈ 200 lb
Therefore, the weight of the cylinder is approximately 200 lb.