A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is very small so that ω(θ=0∘)=0. The ruler has mass m= 200 g and length l= 10 cm. Use g=10 m/s2 for the gravitational acceleration, and the ruler has a uniform mass distribution. Note that there is no friction whatsoever in this problem.

Question

A ruler stands vertically against a wall. It is given a tiny impulse at θ=0∘ such that it starts falling down under the influence of gravity. You can consider that the initial angular velocity is very small so that ω(θ=0∘)=0. The ruler has mass m= 200 g and length l= 10 cm. Use g=10 m/s2 for the gravitational acceleration, and the ruler has a uniform mass distribution. Note that there is no friction whatsoever in this problem.

What is the force exerted by the wall on the ruler when it is at an angle θ=30∘? Express your answer as the x component Fx and the y component Fy (in Newton)

Fx=

Fy=

Answer 1

apply conservation of energy:

U=m*g*hcm
EK= 1/2*I*w^2, I=1/3*m*L^2

Eini= mg(L/2) + 0
Efin= mg(L/2)cos30 + 1/2*I*w^2
solve for Eini=Efin -> w=

any one knows how to answer the other questions?

Answer 2

To find the force exerted by the wall on the ruler at an angle of θ=30∘, we need to analyze the forces acting on the ruler.

The only forces acting on the ruler are the gravitational force and the force exerted by the wall. Since there is no friction, we can neglect it in this problem.

Let's consider the forces acting at the center of mass of the ruler. At θ=30∘, the ruler is at an angle, and we can resolve the forces into x and y components.

1. The gravitational force: The gravitational force acts vertically downward and can be calculated as Fg = mg, where m is the mass of the ruler and g is the acceleration due to gravity. Substituting the given values, we have:
Fg = (0.2 kg) * (10 m/s^2) = 2 N

2. The force exerted by the wall: This force acts along the surface of the ruler and perpendicular to the wall. At an angle of θ=30∘, the force exerted by the wall can be resolved into x and y components.
Fx = -Fw * sin(θ)
Fy = -Fw * cos(θ)

Here, Fx is the x component of the force exerted by the wall, and Fy is the y component.

Since the ruler is in equilibrium, the sum of the forces in the x and y directions must be zero. Therefore, the magnitude of the x component of the force exerted by the wall is equal to the magnitude of the gravitational force: |Fx| = |Fg| = 2 N.

However, the signs of Fx and Fy will depend on the direction of rotation of the ruler. Since we are not given the direction of rotation, we cannot determine the exact values of Fx and Fy without additional information.

Please provide the direction of rotation (clockwise or counterclockwise) to accurately determine the x and y components of the force exerted by the wall.