A uniform plank is 3.0 m long and has a mass of 10 kg. It is secured at its left end in a horizontal position to be used as a di
ving platform. To keep the plank in equilibrium, the point of support must supply: a. an upward force and a clockwise torque b. a downward force and a clockwise torque c. an upward force and a counter-clockwise torque d. a downward force and a counter-clockwise torque e. none of these
1 answer:
To develop the problem it is necessary to take into account the concepts related to Torque and sum of moments.
By torque it is understood that
Where,
F= Force
d = Distance
The value of the given Torque acts from the center of mass causing it to rotate clockwise.
The Force must then be located at the other end down to make a movement opposite the Torque in the center of mass.
I enclose a graph that allows us to understand the problem in a more didactic way.
The correct answer is D.
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To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.
The angular velocity can be described as
Where,
Final Angular Velocity
Initial Angular velocity
Angular acceleration
t = time
The relation between the tangential acceleration is given as,
where,
r = radius.
PART A ) Using our values and replacing at the previous equation we have that
Replacing the previous equation with our values we have,
The tangential velocity then would be,
Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation
Replacing with our values and re-arrange to find
That is equal in revolution to
The linear displacement of the system is,