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Portfolio Problem 2. A particle of mass m slides in a straight line (say along i) on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The = particle is subject to a constant force F = -mai, with a > 0. While sliding on the surface, the particle is also subject to a friction force v Ff = -m fo = −m fov, with fo > 0, i.e., the friction force has constant magnitude mfo and is always opposed to the motion. We also assume fo < a, i.e., |Ff| < |F|. (a) Write the equation of motion when v > 0, and solve it to find v(t) and x(t). How long does it take for the particle to come to a stop? How far does it travel? (b) After coming to a stop, the particle starts sliding backwards with negative velocity. Write the equation of motion in this case, and solve it to find the time at which the particle returns to the original position, x = 0. Show that the final speed at x 0 is smaller than Vo. = Express all your answers in terms of a, fo and Vo.

Portfolio Problem 2. A particle of mass m slides in a straight line (say along i) on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The = particle is subject to a constant force F = -mai, with a > 0. While sliding on the surface, the particle is also subject to a friction force v Ff = -m fo = −m fov, with fo > 0, i.e., the friction force has constant magnitude mfo and is always opposed to the motion. We also assume fo < a, i.e., |Ff| < |F|. (a) Write the equation of motion when v > 0, and solve it to find v(t) and x(t). How long does it take for the particle to come to a stop? How far does it travel? (b) After coming to a stop, the particle starts sliding backwards with negative velocity. Write the equation of motion in this case, and solve it to find the time at which the particle returns to the original position, x = 0. Show that the final speed at x 0 is smaller than Vo. = Express all your answers in terms of a, fo and Vo.

Principles of Physics: A Calculus-Based Text
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
Chapter4: The Laws Of Motion
Section: Chapter Questions
Problem 10P
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Portfolio Problem 2. A particle of mass m slides in a straight line (say along i) on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The = particle is subject to a constant force F = -mai, with a > 0. While sliding on the surface, the particle is also subject to a friction force v Ff = -m fo = −m fov, with fo > 0, i.e., the friction force has constant magnitude mfo and is always opposed to the motion. We also assume fo < a, i.e., |Ff| < |F|. (a) Write the equation of motion when v > 0, and solve it to find v(t) and x(t). How long does it take for the particle to come to a stop? How far does it travel? (b) After coming to a stop, the particle starts sliding backwards with negative velocity. Write the equation of motion in this case, and solve it to find the time at which the particle returns to the original position, x = 0. Show that the final speed at x 0 is smaller than Vo. = Express all your answers in terms of a, fo and Vo.
Transcribed Image Text:Portfolio Problem 2. A particle of mass m slides in a straight line (say along i) on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The = particle is subject to a constant force F = -mai, with a > 0. While sliding on the surface, the particle is also subject to a friction force v Ff = -m fo = −m fov, with fo > 0, i.e., the friction force has constant magnitude mfo and is always opposed to the motion. We also assume fo < a, i.e., |Ff| < |F|. (a) Write the equation of motion when v > 0, and solve it to find v(t) and x(t). How long does it take for the particle to come to a stop? How far does it travel? (b) After coming to a stop, the particle starts sliding backwards with negative velocity. Write the equation of motion in this case, and solve it to find the time at which the particle returns to the original position, x = 0. Show that the final speed at x 0 is smaller than Vo. = Express all your answers in terms of a, fo and Vo.
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