To get up on the roof, a person (mass 70.0 kg) places a 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. What are the magnitudes of the forces on the ladder at the top and bottom?

Solution 17 PE

Step 1 of 5</p>

The magnitude of forces on the acting on the top and bottom of the ladder can be found by writing down the equation for net torque acting on the top of the ladder and net vertical force acting on the bottom of the ladder and applying the conditions of equilibrium to it.

Step 2 of 5</p>

The free body diagram is as shown in the figure below.

Let the length of the ladder be , the distance between the base of the ladder and the house be , distance of the person from the base of the bottom be .

The center of mass of the ladder is at a distance of 2 m from the bottom of the ladder. So, the weight of the ladder is acting downwards at that point. The weight of the person is acting at distance of 3 m from the base of the ladder downwards.

Now, the force acting at the top and bottom of the ladder are the normal reaction acting at the top and bottom of the ladder are and respectively. The friction force exerted by the ground on the ladder is . The ladder makes an angle with the ground.

.

Step 3 of 5</p>

The angle is given by

Where, = distance from the house to bottom of the ladder in m,

= length of the ladder in m

Substituting 2 m for and 6 m for

=

= 70.53o