You are using a 5-m-long ladder to paint the exterior of your house. The point of contact between the ladder and the siding of the house is 4 m above the ground. The ladder has a mass of 18.0 kg. You weigh 56.6 kg and stand three-quarters of the way up the ladder.
(a) Determine the forces exerted by the side wall and the ground on the ladder. (Enter the magnitude only.)
Fside wall = .
Fground = 732 N.
I have found the value of F ground. Please help me in finding the value for F side wall.
To determine the force exerted by the side wall on the ladder, we need to consider the forces acting on the ladder in equilibrium.
First, let's analyze the forces acting on the ladder:
1. The weight of the ladder: Wladder = mass x gravitational acceleration
Wladder = 18.0 kg x 9.8 m/s² = 176.4 N
2. The weight of the person: Wperson = mass x gravitational acceleration
Wperson = 56.6 kg x 9.8 m/s² = 554.68 N
3. The weight of the ladder and the person combined (acting at their center of mass):
Wtotal = Wladder + Wperson
Wtotal = 176.4 N + 554.68 N = 731.08 N
Next, since the ladder is in equilibrium, the sum of the vertical forces must be zero. Therefore, the force exerted by the side wall on the ladder (Fside wall) can be calculated by subtracting the total weight (Wtotal) from the force exerted by the ground (Fground):
Fside wall = Fground - Wtotal
Fside wall = 732 N - 731.08 N = 0.92 N
Thus, the magnitude of the force exerted by the side wall on the ladder is 0.92 N.