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m C A block of mass m slides down a ramp of height hand collides with an identical block that is initially at rest. The two blocks stick together and travel around a loop of radius R without losing contact with the track. Point A is at the top of the loop, point B is at the end of a horizon- tal diameter, and point C is at the bottom of the loop, as shown in the figure above. Assume that friction between the track and blocks is negligible. (a) The dots below represent the two connected blocks at points A, B, and C. Draw free-body dia- grams showing and labeling the forces (not com ponents) exerted on the blocks at each position. Draw the relative lengths of all vectors to reflect the relative magnitude of the forces. Point A Point B Point C (b) For each of the following, derive an expression in terms of m, h, R, and fundamental constants. i. The speed of moving block at the bottom of the ramp, just before it contacts the stationary block ii. The speed of the two blocks immediately after the collision iii. The speed of the two blocks at the top of the loop (point A) 2m sketch a graph of vc as a function of h. Label limiting values on the horizontal axis. B (c) In the scenario shown above, the blocks are connected and the combination of two blocks is released from rest at the top of the incline. The incline can be modeled as a ramp of length Lat an angle from the horizontal, although the curve still exists to ensure speed only changes direction at the bottom of the incline. On the axis below, (d) In which scenario-the colliding blocks in (b) or the connected blocks in (c)-is the minimum initial height required for the blocks to complete the circle least? Briefly justify your answer referring to your free-body diagrams and equations as needed.

m C A block of mass m slides down a ramp of height hand collides with an identical block that is initially at rest. The two blocks stick together and travel around a loop of radius R without losing contact with the track. Point A is at the top of the loop, point B is at the end of a horizon- tal diameter, and point C is at the bottom of the loop, as shown in the figure above. Assume that friction between the track and blocks is negligible. (a) The dots below represent the two connected blocks at points A, B, and C. Draw free-body dia- grams showing and labeling the forces (not com ponents) exerted on the blocks at each position. Draw the relative lengths of all vectors to reflect the relative magnitude of the forces. Point A Point B Point C (b) For each of the following, derive an expression in terms of m, h, R, and fundamental constants. i. The speed of moving block at the bottom of the ramp, just before it contacts the stationary block ii. The speed of the two blocks immediately after the collision iii. The speed of the two blocks at the top of the loop (point A) 2m sketch a graph of vc as a function of h. Label limiting values on the horizontal axis. B (c) In the scenario shown above, the blocks are connected and the combination of two blocks is released from rest at the top of the incline. The incline can be modeled as a ramp of length Lat an angle from the horizontal, although the curve still exists to ensure speed only changes direction at the bottom of the incline. On the axis below, (d) In which scenario-the colliding blocks in (b) or the connected blocks in (c)-is the minimum initial height required for the blocks to complete the circle least? Briefly justify your answer referring to your free-body diagrams and equations as needed.

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter9: Linear Momentum And Collisions
Section: Chapter Questions
Problem 9.1CYU: Check Your Understanding The U.S. Air Force uses “10gs” (an acceleration equal to 109.8m/s2 ) as the...
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m C A block of mass m slides down a ramp of height hand collides with an identical block that is initially at rest. The two blocks stick together and travel around a loop of radius R without losing contact with the track. Point A is at the top of the loop, point B is at the end of a horizon- tal diameter, and point C is at the bottom of the loop, as shown in the figure above. Assume that friction between the track and blocks is negligible. (a) The dots below represent the two connected blocks at points A, B, and C. Draw free-body dia- grams showing and labeling the forces (not com ponents) exerted on the blocks at each position. Draw the relative lengths of all vectors to reflect the relative magnitude of the forces. Point A Point B Point C (b) For each of the following, derive an expression in terms of m, h, R, and fundamental constants. i. The speed of moving block at the bottom of the ramp, just before it contacts the stationary block ii. The speed of the two blocks immediately after the collision iii. The speed of the two blocks at the top of the loop (point A) 2m sketch a graph of vc as a function of h. Label limiting values on the horizontal axis. B (c) In the scenario shown above, the blocks are connected and the combination of two blocks is released from rest at the top of the incline. The incline can be modeled as a ramp of length Lat an angle from the horizontal, although the curve still exists to ensure speed only changes direction at the bottom of the incline. On the axis below, (d) In which scenario-the colliding blocks in (b) or the connected blocks in (c)-is the minimum initial height required for the blocks to complete the circle least? Briefly justify your answer referring to your free-body diagrams and equations as needed.
Transcribed Image Text:m C A block of mass m slides down a ramp of height hand collides with an identical block that is initially at rest. The two blocks stick together and travel around a loop of radius R without losing contact with the track. Point A is at the top of the loop, point B is at the end of a horizon- tal diameter, and point C is at the bottom of the loop, as shown in the figure above. Assume that friction between the track and blocks is negligible. (a) The dots below represent the two connected blocks at points A, B, and C. Draw free-body dia- grams showing and labeling the forces (not com ponents) exerted on the blocks at each position. Draw the relative lengths of all vectors to reflect the relative magnitude of the forces. Point A Point B Point C (b) For each of the following, derive an expression in terms of m, h, R, and fundamental constants. i. The speed of moving block at the bottom of the ramp, just before it contacts the stationary block ii. The speed of the two blocks immediately after the collision iii. The speed of the two blocks at the top of the loop (point A) 2m sketch a graph of vc as a function of h. Label limiting values on the horizontal axis. B (c) In the scenario shown above, the blocks are connected and the combination of two blocks is released from rest at the top of the incline. The incline can be modeled as a ramp of length Lat an angle from the horizontal, although the curve still exists to ensure speed only changes direction at the bottom of the incline. On the axis below, (d) In which scenario-the colliding blocks in (b) or the connected blocks in (c)-is the minimum initial height required for the blocks to complete the circle least? Briefly justify your answer referring to your free-body diagrams and equations as needed.
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