5m ladder leans against frictionless wall. point of contact is 4m above the ground. ladder has uniform mass of 15kg. determine forces by ground and the wall on the ladder
To determine the forces exerted by the ground and the wall on the ladder, we need to consider the equilibrium conditions of the ladder. Since the ladder is not moving, the sum of the forces and torques acting on it must be zero.
1. Start by drawing a free body diagram of the ladder. Label the forces exerted by the ground and the wall as FG and FW, respectively.
2. Considering the forces, we know that there are no horizontal forces acting on the ladder because it is in equilibrium. Therefore, FG and FW only have vertical components.
3. The weight of the ladder acts downward and can be calculated as W = m * g, where m is the mass of the ladder (15 kg) and g is the acceleration due to gravity (9.8 m/s^2). So W = 15 kg * 9.8 m/s^2 = 147 N.
4. The vertical component of the force exerted by the ground (FG) must balance the weight of the ladder. Since the ladder is in equilibrium, the vertical component of FG is equal to the weight, FG = 147 N.
5. The force exerted by the wall (FW) acts perpendicular to the wall. Since there are no horizontal forces acting on the ladder, the vertical component of FW must balance the weight of the ladder as well. Therefore, FW = 147 N.
In conclusion, the force exerted by both the ground and the wall on the ladder is 147 N, upward, to balance the weight of the ladder.