The Ladder is 5 m long and weighs 180N. The guy weighs 800N, and stops 1m horizontally up the ladder. The bottom of the ladder rest on a horizontal stone ledge at 53.1 degree.
Find the normal and he frictional force at the base.
HELP!!!
To find the normal and frictional force at the base of the ladder, we need to analyze the forces acting on the ladder and the guy.
First, let's break down the forces acting on the ladder. We have the weight of the ladder acting vertically downward, which is 180N. We also have the reaction force from the stone ledge acting vertically upward, which is the normal force.
To find the normal force, we can use the fact that the ladder is in equilibrium. The sum of the vertical forces must be zero. Therefore, the normal force equals the weight of the ladder, which is 180N.
Next, let's consider the forces acting on the guy. We have the weight of the guy acting downward, which is 800N. We also have the horizontal component of the reaction force from the stone ledge acting horizontally inward, and the frictional force acting horizontally outward.
To find the frictional force, we first need to calculate the horizontal component of the reaction force. We can use trigonometry to determine this. The angle between the ladder and the horizontal ground is given as 53.1 degrees. Therefore, the horizontal component of the reaction force is:
Horizontal component = Normal force * cos(angle)
Horizontal component = 180N * cos(53.1 degrees)
Now we can determine the frictional force. Since the ladder is in equilibrium, the sum of the horizontal forces must be zero. The frictional force and the horizontal component of the reaction force should be equal in magnitude but opposite in direction. Therefore, the frictional force is:
Frictional force = - Horizontal component
Frictional force = - (180N * cos(53.1 degrees))
Note: The negative sign indicates that the direction of the force is opposite to the horizontal component of the reaction force.
So, to summarize:
Normal force = 180N
Frictional force = - (180N * cos(53.1 degrees))
Plug in the values for the angle and calculate the frictional force.