# Classical Mechanics Physics

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= 250 g and length l= 30 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. (See figure)

(a) What is the angular speed of the ruler ω when it is at an angle θ=30∘? (in radians/sec)

ω=

(b) 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=

(c) At what angle θ0 will the falling ruler lose contact with the wall? (0≤θ0≤90∘; in degrees) [hint: the ruler loses contact with the wall when the force exerted by the wall on the ruler vanishes.]

θ0=

1. 👍 0
2. 👎 0
3. 👁 187
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?

1. 👍 0
2. 👎 0
2. Can you please elaborate.. thanx

1. 👍 0
2. 👎 0
3. I=1/3*m*L^2
Eini= mg(L/2) + 0
Efin= mg(L/2)cos30 + 1/2*I*w^2
Eini=Efin ->
w=sqrt(3*g (1-cos(theta))/L)

b)
alpha=3*mg/2*sin(theta)/L
ax = -L/2*sin(theta) w^2 + L/2*cos(theta) alpha
Fx=m*ax
Fy=m*g*cos(theta)-m*w^2*(L/2)

c)
cos(theta)=2/3
theta=48.19

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

A playground is on the flat roof of a city school, 5.8 m above the street below (see figure). The vertical wall of the building is h = 7.30 m high, to form a 1.5-m-high railing around the playground. A ball has fallen to the

2. ### physics

A spring with k = 53 N/m hangs vertically next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks

3. ### physics!!

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed –v. The impulse imparted to the ball by the wall is 1) 2mv 2)mv 3)-mv 4)zero 5)-2mv

4. ### Physics

A spring with 50 N/m hangs vertically next to a ruler. The end of the spring is next to the 21-cm mark on the ruler.If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler

1. ### PHYSICS

A Hammer weighing 3kg strikes the head of a nail with a speed of 2m/s and drives it by 1cm into the wall. find the impulse?

2. ### physics

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed –v. The impulse imparted to the ball by the wall is

3. ### algebra

Essam traced his ruler on graph paper. He kept the edge of the ruler on the paper while he flipped the ruler over. Then, he traced the ruler again. What type of transformation did he perform? A. duplication B. translation C.

4. ### Math

A 25-foot ladder stands against a vertical wall at an angle of n degrees with the ground. If sin n = 4 / 5, how far is the base of the ladder from the wall? A. 12 B. 13 C. 14 D. 15 E. 16

1. ### physics

A 0.060-kg handball is thrown straight toward a wall with a speed of 9 m/s. It rebounds straight backward at a speed of 6.7 m/s (a) What impulse is exerted on the wall? magnitude 0.942 kg·m/s (b) If the ball is in contact with

2. ### Physics

Joshua has a mass of 60kg and stands next to a wall ona frictionless skateboard. If he pushes the wall with a force of 30N, how hard does the wall push on him? Show that Joshua accelerates at .5 m/s2 away from the wall.

3. ### calculus

A painting is hung on a wall in such a way that its upper and lower edges are 10 ft and 7ft above the floor, respectively. An observer whose eyes are 5 ft above the floor stands x feet from the wall. How far away should the

4. ### maths

If a 10m ladder stands 1.25m from a wall, what is it's reach?