A uniform beam AB of mass 84.78 kg rest against the smooth wall at A and the rough horizontal floor at B. The coefficient of static friction between the beam and the horizontal floor is U=0.249.

Calculate the magnitude of the horizontal force P, in N, such that the end B has IMPENDING MOTION TO THE LEFT. Assume g = 9.81 m/s^2.

To calculate the magnitude of the horizontal force P required for end B of the beam to have impending motion to the left, we can use the principles of equilibrium and friction.

Step 1: Identify the forces acting on the beam:
- Weight of the beam acting vertically downwards (W)
- Normal force exerted by the floor acting vertically upwards (N)
- Horizontal force applied at point B (P)
- Frictional force acting on the beam (f)

Step 2: Determine the force components:
- The weight of the beam (W) can be calculated using the formula W = mass * gravity.
W = 84.78 kg * 9.81 m/s^2

Step 3: Calculate the normal force (N):
- The normal force (N) can be determined by considering the equilibrium of forces in the vertical direction. In this case, the weight (W) is balanced by the normal force (N).
W = N

Step 4: Calculate the frictional force (f):
- The coefficient of static friction (U) is given as 0.249, and the frictional force (f) can be calculated using the formula f = U * N.
f = 0.249 * N

Step 5: Calculate the net horizontal force:
- Since the beam is at rest, the net horizontal force acting on the beam is zero. This means that the horizontal force applied at point B (P) must be balanced by the frictional force (f).
P = f

Step 6: Substitute the values and calculate P:
- Substitute the previously calculated values of N and f into the equation P = f.
P = 0.249 * N

- Finally, substitute the value of N from step 3 into the equation to get the value of P.

By following these steps, you can determine the magnitude of the horizontal force P required to initiate motion to the left.