Question

A uniform plank of mass 2.53 kg and length 21.5 cm is pivoted at one end. A spring of force constant 403 N/m is attached to the center of the plank, as shown in the figure. The height of the pivot has been adjusted so that the plank will be in equilibrium when it is horizontally oriented.

Find the period of small oscillation about the equilibrium point. Answer in units of s.

Answer #1

A stick of mass M and length L is pivoted at one end. A
small mass m<M is attached to the right-hand end of the stick.
The stick is held horizontally and released from rest.
Given that the rotational inertia of a uniform rod
pivoted around one end is 1/3ML^2, determine the rotational inertia
of the described system.
Calculate the angular velocity of the system when it
reaches a vertical position. You cannot use rotational kinematics
here because angular acceleration...

The pendulum in the figure consists of a uniform disk with
radius r = 11.0 cm and mass 470 g attached to a uniform rod with
length L = 640 mm and mass 240 g. (a) Calculate the rotational
inertia of the pendulum about the pivot point. (b) What is the
distance between the pivot point and the center of mass of the
pendulum? (c) Calculate the period of oscillation

A uniform plank of length 6.00 m and mass 27.0 kg rests
horizontally across two horizontal bars of a scaffold. The bars are
4.50 m apart, and 1.50 m of the plank hangs over one side of the
scaffold. Draw a free-body diagram of the plank.
How far can a painter with a mass of 74.0 kg walk on the
overhanging part of the plank before it tips?

A 1.40 kg box rests on a plank that is inclined at an angle of
29° above the horizontal. The upper end of the box is attached to a
spring with a force constant of 21 N/m, as shown in the figure. If
the coefficient of static friction between the box and the plank is
0.80, what is the maximum amount the spring can be compressed and
the box remain at rest?

A uniform plank of length 2 m and mass 30 kg is supported by
three rope, indicated by the blue vectors in figure P8.27. fine the
tension of each rope when a 700N person is d= 0.500 from the left
end

A uniform rod of mass M and length L is pivoted at one
end. The rod is left to freely rotate under the influence of its
own weight. Find its angular acceleration α when it makes
an angle 30° with the vertical axis. Solve for M=1 Kg, L=1 m,
take g=10 m s-2. Hint: Find the center of mass for the rod, and
calculate the torque, then apply Newton as τ= Ι·α

5) A 2kg metal bar with 3 meters length is pivoted to the wall
on one end and it is attached with a string on the other end to 4
meters above the pivot. A 0.5 kg additional mass is placed on the
bar 1.2 meters away from the pivot. Calculate the Tension.
Calculate the reaction force of the pivot both as a vector and as
magnitude.

A uniform thin stick of length L=3.00 m and mass m=2.00 kg is
undergoing small oscillations about a pivot point x away from its
center of mass. For the oscillation period to be the minimum
possible value, what should be the value of x? Enter the value in
meters.

A uniform thin stick of length L=2.25 m and mass m=1.75 kg is
undergoing small oscillations about a pivot point x away from its
center of mass. For the oscillation period to be the minimum
possible value, what should be the value of x? Enter the value in
meters.

A uniform rod of mass M and length L is pivoted at one end. The
rod is left to freely rotate under the influence of its own weight.
Find its angular acceleration α when it makes an angle 30° with the
vertical axis. Solve for M=1 Kg, L=1 m, take g=10 m s-2. Your
answer in X.X rad s-2. Hint: Find the center of mass for the rod,
and calculate the torque, then apply Newton as τ= Ι·α

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