A 15 m ladder with a mass of 51 kg is leaning against a frictionless wall, which makes an angle of 60 degrees with the horizontal. What is the horizontal force exerted by the ground on the ladder when an 81 kg object is 4.0 m from the bottom?

266.5 newton

Explanation:

Weight of first object = 51 kg * 9.81

= 500 N

Weight of second object = 81 kg * 9.81

= 794.61 N

As length of ladder is 15 m, the center of mass will be at 7.5 m.

Level arm is always perpendicular to the force. So the level of arm is at

7.5 sin θ.

τ (wall) = τ (first object) + τ (second object)

N cos 30 * 15 = 794.61 sin 30 * 4 + (500 sin 30 * 7.5)

13 N = 1589.22 + 1875

13 N = 3464.22

N = 266.5 newton