Concept explainers
Review. A thin, uniform, rectangular signboard hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kg, and its vertical dimension is 50.0 cm. The sign is swinging without friction, so it is a tempting target for children armed with snowballs. The maximum
(a)
The angular speed of the sign immediate before the collision.
Answer to Problem 11.38P
The angular speed of the sign immediate before the collision is
Explanation of Solution
The mass of sign is
Consider figure given below.
Figure (I)
The height of the sign is calculated as,
Here,
The formula for the conservation of the energy is,
Here,
The formula to calculate initial moment of inertia is,
Substitute
Substitute
Conclusion:
Therefore, the angular speed of the sign immediate before the collision is
(b)
The angular speed of the sign immediate after the collision.
Answer to Problem 11.38P
The angular speed of the sign immediate after the collision is
Explanation of Solution
The formula for the conservation of the angular momentum is,
Here,
The formula to calculate final moment of inertia is,
Substitute
Substitute
Conclusion:
Therefore, the angular speed of the sign immediate after the collision is
(c)
The maximum angle.
Answer to Problem 11.38P
The maximum angle is
Explanation of Solution
The formula distance of the centre of mass from the axis of rotation is,
Substitute
The conservation of mechanical energy is,
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the maximum angle is
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Chapter 11 Solutions
Physics For Scientists And Engineers, Volume 2
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