A ladder of mass 20kg and length 5m can be held up against a wall because the wall exerts a normal force against it. The grass has a coefficient of a static friction of 0.35. find the normal force of the wall against the ladder.
To find the normal force exerted by the wall against the ladder, we need to consider the forces acting on the ladder.
Let's break it down into two parts: the forces acting along the vertical direction (up and down) and the forces acting along the horizontal direction (left and right).
First, let's consider the forces acting along the vertical direction:
1. The weight of the ladder: The weight is given by the formula weight = mass × gravitational acceleration. The mass of the ladder is given as 20 kg. The gravitational acceleration is approximately 9.8 m/s². Therefore, the weight of the ladder is 20 kg × 9.8 m/s² = 196 N (Newtons). This force is pulling the ladder downward.
2. The normal force: This is the force exerted by the wall against the ladder, perpendicular to the surface of the wall. Since the ladder is in equilibrium (not moving), the normal force must be equal in magnitude but opposite in direction to the weight of the ladder. Therefore, the normal force is also 196 N, but directed upward. This force helps to support the ladder.
Now, let's consider the forces acting along the horizontal direction:
1. The static friction force: The static friction force prevents the ladder from sliding horizontally. The static friction force can be calculated using the formula friction force = coefficient of static friction × normal force. The coefficient of static friction is given as 0.35. The normal force has already been determined as 196 N. Therefore, the static friction force is 0.35 × 196 N = 68.6 N. This force acts in the opposite direction of any horizontal force trying to move the ladder.
In summary:
- The normal force exerted by the wall against the ladder is 196 N (upward).
- The static friction force between the ladder and the ground is 68.6 N (opposite to any horizontal force trying to move the ladder).