A 10.0 m long ladder weighing 50.0 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50.0° angle with the ground find the coefficient of static friction between the ladder and ground. The ladder is in equilibrium. This means that the torque around ANY pivot point must be zero. In problems like this, you can pick the pivot point of your choice, and still solve for the correct forces. However, there is typically a choice for the pivot point that makes the problem solving steps possible or at least easier. This will depend on the problem, but often depends on the fact that the torque due to a force at the pivot point is zero. This lets you ignore those torque terms in your calculations. a. What is the best choice of pivot point for this problem? Select one: A. The base of the ladder B. The center of mass of the ladder C. The top of the ladder By selecting the base of the ladder, you can ignore the torque due to both the normal force from the ground on the ladder and the the static friction force from the ground on the ladder. b. The weight of the ladder will cause a torque about the base of the ladder. What is the magnitude of this torque? (Give your answer in N m.) Recall: ?=??????τ=rFsinϕ Where ?ϕ is the angle between the r vector and the force vector. You have the torque due to the weight of the ladder. Because the ladder is in equilibrium, the torque due to the normal force from the wall on the ladder must be equal to this torque. (This is why it was convenient to use the base of the ladder as the pivot. We can ignore the torques due to both forces at the base. c. What is the normal force from the wall on the ladder? (Give your answer in N.)
Rotational Equilibrium And Rotational Dynamics
In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.
Equilibrium of Forces
The tension created on one body during push or pull is known as force.
A 10.0 m long ladder weighing 50.0 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50.0° angle with the ground find the coefficient of static friction between the ladder and ground.
The ladder is in equilibrium. This means that the torque around ANY pivot point must be zero. In problems like this, you can pick the pivot point of your choice, and still solve for the correct forces. However, there is typically a choice for the pivot point that makes the problem solving steps possible or at least easier. This will depend on the problem, but often depends on the fact that the torque due to a force at the pivot point is zero. This lets you ignore those torque terms in your calculations.
a. What is the best choice of pivot point for this problem?
The base of the ladder
The center of mass of the ladder
The top of the ladder
By selecting the base of the ladder, you can ignore the torque due to both the normal force from the ground on the ladder and the the static friction force from the ground on the ladder.
b. The weight of the ladder will cause a torque about the base of the ladder. What is the magnitude of this torque? (Give your answer in N m.)
Recall: ?=??????τ=rFsinϕ
Where ?ϕ is the angle between the r vector and the force vector.
You have the torque due to the weight of the ladder. Because the ladder is in equilibrium, the torque due to the normal force from the wall on the ladder must be equal to this torque. (This is why it was convenient to use the base of the ladder as the pivot. We can ignore the torques due to both forces at the base.
c. What is the normal force from the wall on the ladder? (Give your answer in N.)
Hint: Use the torque equation to solve for the force.
Next, consider the net force in the x direction. What is magnitude of the static friction force from the ground on the ladder? (Give your answer in N.)
d. Finally, we can find the coefficient of static friction. What is this coefficient?
Note: you will need to find the normal force by considering the net force in the y direction. Then you can use the equation for static friction:
If the ladder is is at the maximum angle: ??=???
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