A construction worker attempts to lift a uniform beam off the floor and raise it to a vertical position. The beam is long and weighs . At a certain instant the worker holds the beam momentarily at rest with one end at distance above the floor, as shown in Fig. 12-75, by exerting a force on the beam, perpendicular to the beam. (a) What is the magnitude P? (b) What is the magnitude of the (net) force of the floor on the beam? (c) What is the minimum value the coefficient of static friction between beam and floor can have in order for the beam not to slip at this instant?
a) The magnitude of the applied force,
b) Net force exerted by the floor on beam,
c) The minimum value of the coefficient of static friction,
The length of the beam is .
Weight of beam is .
Given the distance from the floor is
Using the condition for the static equilibrium, you can write the equation for torque. Solving this, you would get force. Using this value of force, you can find the coefficient of friction. The equations are given below
For the angle between floor and beam
As the beam is diagonal of a triangle and given height is its one side.
As the system is in equilibrium, we can write the moment of force as
If we see the diagram, we can write,
Question: In Fig 12-30, trying to get his car out of mud, a man ties one end of a rope around the front bumper and the other end tightly around a utility pole 18 m away. He then pushes sideways on the rope at its midpoint with a force of 550 N , displacing the center of the rope 0.30 m , but the car barely moves. What is the magnitude of the force on the car from the rope? (The rope stretches somewhat.)
In Fig. 12-69, a package of mass m hangs from a short cord that is tied to the wall via cord 1 and to the ceiling via cord 2. Cord 1 is at angle with the horizontal; cord 2 is at angle. (a) For what value of is the tension in cord 2 minimized? (b) In terms of mg, what is the minimum tension in cord 2
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