Physics help?

Question

A uniform ladder of length 8.00 m and mass 51.0 kg rests against a frictionless wall, making an angle of 60º with the horizontal. The ladder is on the verge of slipping when an 81.6-kg fireman climbs 4.80 m along it. Find the horizontal and vertical forces exerted on the foot of the ladder by the ground, and the coefficient of static friction between the ladder and the ground.

Answer 1

Step 1:

(a)

The Length of the ladder is 8 m.

Mass of the ladder m = 51.0 kg.

Angle made by the ladder with respect to the ground is 60°.

Mass of the fireman M = 81.6 kg.

Distance travelled by the fireman is 4.80 m.

Free body diagram of the data is

Here F_Gx is the frictional force,  F_Gy is the Normal force and F_W is the force exerted by the wall.

Vertical Force :

Sum of the forces in the vertical direction is equal to zero.

Vertical Force F_Gx = 1299.48 N.

Step 2:

Horizontal Force :

Sum of the forces in the horizontal direction is equal to zero.

     (Negative sign indicates opposite direction)   (1)

To calculate Force exerted by the wall, consider sum of torque is zero.

                                                  (2)

Torque exerted by the wall along the ladder.

Angle made by the ladder with respect to the wall is .

Torque exerted by the wall N-m.

Torque exerted by the ladder:

Torque exerted by the ladder N-m.

Torque exerted by the person travelling along the ladder:

Torque exerted by the person travelling along the ladder N-m.

Comments

Step 3:

Substitute the values of the torque in equation (2).

Force exerted by the wall is F_W = 1263.89 N.

Substitute F_W = 1263.89 N in equation (1).

Horizontal force F_Gy = 1263.89 N.

Solution:

Horizontal force F_Gx = 1299.48 N N.

Vertical Force F_Gy = 1263.89 N.

Answer 2

Step 1:

(b)

Torque exerted by the ladder due to friction :

Torque exerted by the ladder :

Torque due to wall :

The clockwise torque balance the counterclockwise torque:

Cancel the common terms.

Coefficient of static friction is 0.6350.

Solution:

Coefficient of static friction is 0.6350.