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Two identical, thin boards are hinged together at an end as shown below. The length of each board is l, and the total mass of each is m. Initially, one board hangs down freely from the hinge while the other is held at angle 0 by a horizontal string. Ignore any friction. (a.) Find the string's tension. Answer: mg tan 0 (b.) If the string is broken, what is the incoming board's kinetic energy Ko just before impact? Answer: mal (1 – cos 0) (c.) Find the incoming board's angular momentum L just before impact. Make use of Eqn. (2) to minimize the algebra. Answer: L2 =m²gl° (1 – cos 0) 2 - (d.) Show that the kinetic energy of both boards just after the impact is Ko/2. Assume the collision is completely inelastic. Hint: Apply Eqn. (2) to minimize the algebra.

Two identical, thin boards are hinged together at an end as shown below. The length of each board is l, and the total mass of each is m. Initially, one board hangs down freely from the hinge while the other is held at angle 0 by a horizontal string. Ignore any friction. (a.) Find the string's tension. Answer: mg tan 0 (b.) If the string is broken, what is the incoming board's kinetic energy Ko just before impact? Answer: mal (1 – cos 0) (c.) Find the incoming board's angular momentum L just before impact. Make use of Eqn. (2) to minimize the algebra. Answer: L2 =m²gl° (1 – cos 0) 2 - (d.) Show that the kinetic energy of both boards just after the impact is Ko/2. Assume the collision is completely inelastic. Hint: Apply Eqn. (2) to minimize the algebra.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Two identical, thin boards are hinged together at an end as illustrated. The length of each board is \( l \), and the total mass of each is \( m \). Initially, one board hangs down freely from the hinge while the other is held at angle \( \theta_0 \) by a horizontal string. Ignore any friction. (a.) Find the string’s tension. **Answer:** \( \frac{mg}{2} \tan \theta_0 \) (b.) If the string is broken, what is the incoming board’s kinetic energy \( K_0 \) just before impact? **Answer:** \( \frac{mgl}{2} (1 - \cos \theta_0) \) (c.) Find the incoming board’s angular momentum \( L \) just before impact. Make use of Eqn. (2) to minimize the algebra. **Answer:** \( L^2 = \frac{1}{3} m^2 g l^3 (1 - \cos \theta_0) \) (d.) Show that the kinetic energy of both boards just after the impact is \( K_0/2 \). Assume the collision is completely inelastic. Hint: Apply Eqn. (2) to minimize the algebra. (e.) To what angle do the boards rise after the collision? **Answer:** \( \arccos \left( \frac{3}{4} + \frac{1}{4} \cos \theta_0 \right) \) **Diagram Description:** The diagram shows two boards connected at a hinge. One board is vertical, hanging down, and the other board is at an angle \( \theta_0 \) to the horizontal, held by a string.
Transcribed Image Text:Two identical, thin boards are hinged together at an end as illustrated. The length of each board is \( l \), and the total mass of each is \( m \). Initially, one board hangs down freely from the hinge while the other is held at angle \( \theta_0 \) by a horizontal string. Ignore any friction. (a.) Find the string’s tension. **Answer:** \( \frac{mg}{2} \tan \theta_0 \) (b.) If the string is broken, what is the incoming board’s kinetic energy \( K_0 \) just before impact? **Answer:** \( \frac{mgl}{2} (1 - \cos \theta_0) \) (c.) Find the incoming board’s angular momentum \( L \) just before impact. Make use of Eqn. (2) to minimize the algebra. **Answer:** \( L^2 = \frac{1}{3} m^2 g l^3 (1 - \cos \theta_0) \) (d.) Show that the kinetic energy of both boards just after the impact is \( K_0/2 \). Assume the collision is completely inelastic. Hint: Apply Eqn. (2) to minimize the algebra. (e.) To what angle do the boards rise after the collision? **Answer:** \( \arccos \left( \frac{3}{4} + \frac{1}{4} \cos \theta_0 \right) \) **Diagram Description:** The diagram shows two boards connected at a hinge. One board is vertical, hanging down, and the other board is at an angle \( \theta_0 \) to the horizontal, held by a string.
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