Two identical, thin boards are hinged together at an end as shown below. The lengthof each board is l, and the total mass of each is m. Initially, one board hangs downfreely from the hinge while the other is held at angle 00 by a horizontal string. Ignoreany friction.(a.) Find the string's tension. Answer: "mg tan 00(b.) If the string is broken, what is the incoming board's kinetic energy Ko just beforeimpact? Answer: mgl (1 – cos 60)2(c.) Find the incoming board's angular momentum L just before impact. Make use ofEqn. (2) to minimize the algebra.Answer: L2 = m²gl® (1 – cos 0)(d.) Show that the kinetic energy of both boards just after the impact is Ko/2. Assumethe 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 (3/4 + 1/4 cos 00)

Torque is the rotational equivalent of linear force that causes an object to rotate about an axis.…

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.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.16P

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