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Consider a simple pendulum where a wooden block of mass M is suspended from a support by a rigid rod of length 7. A bullet of mass m moving horizontally with speed s strikes the block and becomes embedded in it. to determine the speed of the bullet. (a) If the velocity of the block is vo immediately after impact, show that m+M m -VO- (b) If the maximum angle reached by the rod after the collision is a, use conservation of energy after the impact to show that v=2gl (1-cosa), and hence find the speed of the bullets in terms of g, 1, m, M and a. (c) Write the equations of motion in polar coordinates assuming now that, after the collision the block is subiect to a constant friction force E always opposite the direction

Consider a simple pendulum where a wooden block of mass M is suspended from a support by a rigid rod of length 7. A bullet of mass m moving horizontally with speed s strikes the block and becomes embedded in it. to determine the speed of the bullet. (a) If the velocity of the block is vo immediately after impact, show that m+M m -VO- (b) If the maximum angle reached by the rod after the collision is a, use conservation of energy after the impact to show that v=2gl (1-cosa), and hence find the speed of the bullets in terms of g, 1, m, M and a. (c) Write the equations of motion in polar coordinates assuming now that, after the collision the block is subiect to a constant friction force E always opposite the direction

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Consider a simple pendulum where a wooden block of mass M is suspended from a support by a rigid rod of length 1. A bullet of mass m moving horizontally with speed s strikes the block and becomes embedded in it. to determine the speed of the bullet. (a) If the velocity of the block is vo immediately after impact, show that m+M m -VO- (b) If the maximum angle reached by the rod after the collision is a, use conservation of energy after the impact to show that v=2gl (1-cosa), and hence find the speed of the bullet s in terms of g, 1, m, M and a. (c) Write the equations of motion in polar coordinates assuming now that, after the collision, the block is subject to a constant friction force Fo always opposite the direction of the velocity, i.e., the force is F = Fov/v). Compute the work done by all the existing forces while the block moves from 0 = 0 to 0 = a.
Transcribed Image Text:Consider a simple pendulum where a wooden block of mass M is suspended from a support by a rigid rod of length 1. A bullet of mass m moving horizontally with speed s strikes the block and becomes embedded in it. to determine the speed of the bullet. (a) If the velocity of the block is vo immediately after impact, show that m+M m -VO- (b) If the maximum angle reached by the rod after the collision is a, use conservation of energy after the impact to show that v=2gl (1-cosa), and hence find the speed of the bullet s in terms of g, 1, m, M and a. (c) Write the equations of motion in polar coordinates assuming now that, after the collision, the block is subject to a constant friction force Fo always opposite the direction of the velocity, i.e., the force is F = Fov/v). Compute the work done by all the existing forces while the block moves from 0 = 0 to 0 = a.
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