Tutorial Exercise A bead with a hole through it slides on a wire track. The wire is threaded through the hole in the bead, and the bead slides without friction around a loop-the-loop (see figure below). The bead is released from rest at a height h = 3.05R. R (a) What is its speed at point Ⓐ? (b) How large is the normal force on the bead at point A if its mass is 5.95 g? Part 1 of 4 - Conceptualize is Since the bead is released above the top of the loop, it starts with enough potential energy to reach point Ⓐ and still have excess kinetic energy. The energy of the bead at point proportional to h and g. If it is moving relatively slowly, the track will exert an upward force on the bead, but if it is whipping around quickly, the normal force will push it toward the center of the loop. Part 2 of 4 - Categorize The speed at the top of the loop can be found from the conservation of energy for the bead-track-Earth system and the normal force can be found from Newton's second law. Part 3 of 4 - Analyze (a) We define the bottom of the loop as the zero level for the gravitational potential energy. For the total energy of the system at point Ⓐ, we have U¡ + K¡ = Uƒ + Kf. Now we know that U; mgh and Ki = 0 because the bead starts from rest at height h. At point Ⓐ, the bead is at height 3.05 = Your response differs from the correct answer by more than 10%. Double check your calculations.R with speed v, so we have mgh + 0 = mg 3.05 Your response differs from the correct answer by more than 10%. Double check your calculations.R) + Substituting the given expression for h in terms of R, gives mg 3.05 R) = mg ( 3.05 × 를까? S.R) + 를까? Your response differs from the correct answer by more than 10%. Double check your calculations.R) + Now we can solve for v in terms of R and g. v2 3.05 = Your response differs from the correct answer by more than 10%. Double check your calculations. 3.05 V = × Your response differs from the correct answer by more than 10%. Double check your calculations.gR
Tutorial Exercise A bead with a hole through it slides on a wire track. The wire is threaded through the hole in the bead, and the bead slides without friction around a loop-the-loop (see figure below). The bead is released from rest at a height h = 3.05R. R (a) What is its speed at point Ⓐ? (b) How large is the normal force on the bead at point A if its mass is 5.95 g? Part 1 of 4 - Conceptualize is Since the bead is released above the top of the loop, it starts with enough potential energy to reach point Ⓐ and still have excess kinetic energy. The energy of the bead at point proportional to h and g. If it is moving relatively slowly, the track will exert an upward force on the bead, but if it is whipping around quickly, the normal force will push it toward the center of the loop. Part 2 of 4 - Categorize The speed at the top of the loop can be found from the conservation of energy for the bead-track-Earth system and the normal force can be found from Newton's second law. Part 3 of 4 - Analyze (a) We define the bottom of the loop as the zero level for the gravitational potential energy. For the total energy of the system at point Ⓐ, we have U¡ + K¡ = Uƒ + Kf. Now we know that U; mgh and Ki = 0 because the bead starts from rest at height h. At point Ⓐ, the bead is at height 3.05 = Your response differs from the correct answer by more than 10%. Double check your calculations.R with speed v, so we have mgh + 0 = mg 3.05 Your response differs from the correct answer by more than 10%. Double check your calculations.R) + Substituting the given expression for h in terms of R, gives mg 3.05 R) = mg ( 3.05 × 를까? S.R) + 를까? Your response differs from the correct answer by more than 10%. Double check your calculations.R) + Now we can solve for v in terms of R and g. v2 3.05 = Your response differs from the correct answer by more than 10%. Double check your calculations. 3.05 V = × Your response differs from the correct answer by more than 10%. Double check your calculations.gR
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter7: Conservation Of Energy
Section: Chapter Questions
Problem 3P: Review. A bead slides without friction around a loop-the-loop (Fig. P7.3). The bead is released from...
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