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I1. A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy given by U(x) = ax where a = 1.20]/m*. What is the force (magnitude and direction) when the particle is at x = -0.80m?

I1. A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy given by U(x) = ax where a = 1.20]/m*. What is the force (magnitude and direction) when the particle is at x = -0.80m?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
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ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter7: Conservation Of Energy
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11. A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy given by U(x) = ax* where a = 1.20]/m*. What is the force (magnitude and direction) when the particle is at x = -0.80m? 12. A marble moves along the x-axis. The potential-energy function is shown in Figure. (a) at which of the labeled x-coordinates is the force on the marble zero? (b) Which of the labeled x-coordinates is a position of stable equilibrium? (c) Which of the labeled x- coordinates is a position of unstable equilibrium? U0) 4.0 2.0 ds (m) 150 2.5 -2.0 13. Figure below showing potential energy function of a particle. Rank the magnitude of force in the region AB, CD, EF and GH. What value must the total mechanical energy Ene of the particle not exceed if the particle is to be trapped between A and D? AB GH Power 14. In three situations a single force acts on a moving particle. Here are the velocities and forces: (i) i = (-4) m/s and F = (61 – 205) N; (ii) i = (2i – 3) m/s and F = (-2j + 7k) N; (iii) i = (-31 + ) m/s and F = (21 + 6) N: Rank the situations according to the rate at which energy is being transferred, highest to lowest. 15. What is the resistive force on a cyclist who has leg muscles of power 200 W each and who reaches a top speed of 10 ms' on a level road?
Transcribed Image Text:11. A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces potential energy given by U(x) = ax* where a = 1.20]/m*. What is the force (magnitude and direction) when the particle is at x = -0.80m? 12. A marble moves along the x-axis. The potential-energy function is shown in Figure. (a) at which of the labeled x-coordinates is the force on the marble zero? (b) Which of the labeled x-coordinates is a position of stable equilibrium? (c) Which of the labeled x- coordinates is a position of unstable equilibrium? U0) 4.0 2.0 ds (m) 150 2.5 -2.0 13. Figure below showing potential energy function of a particle. Rank the magnitude of force in the region AB, CD, EF and GH. What value must the total mechanical energy Ene of the particle not exceed if the particle is to be trapped between A and D? AB GH Power 14. In three situations a single force acts on a moving particle. Here are the velocities and forces: (i) i = (-4) m/s and F = (61 – 205) N; (ii) i = (2i – 3) m/s and F = (-2j + 7k) N; (iii) i = (-31 + ) m/s and F = (21 + 6) N: Rank the situations according to the rate at which energy is being transferred, highest to lowest. 15. What is the resistive force on a cyclist who has leg muscles of power 200 W each and who reaches a top speed of 10 ms' on a level road?
7. A 40 kg box initially at rest is pushed 5.0m along a rough horizontal floor with a constant applied horizontal force of 130N. If the coefficient of friction between the box and floor is 0.30, find (a) the work done by the applied force, (b) the energy lost due to friction, (e) the change in kinetic energy of the box, and (d) the final speed of the box. 8. A pendulum consists of a 2.0kg stone on a 4.0m string of negligible mass. The stone has a speed of 8.0 m/s when it passes its lowest point. What is the speed when the string is at 60° to the vertical? 60 4.0 m 20 kg 80 mis (a) (b) 9. A particle moves along the x-axis while acted on by a single conservative force parallel to the x- axis. The force coresponds to the potential-energy function graphed in the Figure. The particle is released from rest at point A. (a) What is the direction of the force on the particle when it is at point A? (b) At point B? (c) At what value of x is the kinetic energy of the particle a maximum? (d) What is the force on the particle when it is at point C? (e) What is the largest value of x reached by the particle during its motion? (f) What value or values of x correspond to points of stable equilibrium? (g) Of unstable equilibrium? ed
Transcribed Image Text:7. A 40 kg box initially at rest is pushed 5.0m along a rough horizontal floor with a constant applied horizontal force of 130N. If the coefficient of friction between the box and floor is 0.30, find (a) the work done by the applied force, (b) the energy lost due to friction, (e) the change in kinetic energy of the box, and (d) the final speed of the box. 8. A pendulum consists of a 2.0kg stone on a 4.0m string of negligible mass. The stone has a speed of 8.0 m/s when it passes its lowest point. What is the speed when the string is at 60° to the vertical? 60 4.0 m 20 kg 80 mis (a) (b) 9. A particle moves along the x-axis while acted on by a single conservative force parallel to the x- axis. The force coresponds to the potential-energy function graphed in the Figure. The particle is released from rest at point A. (a) What is the direction of the force on the particle when it is at point A? (b) At point B? (c) At what value of x is the kinetic energy of the particle a maximum? (d) What is the force on the particle when it is at point C? (e) What is the largest value of x reached by the particle during its motion? (f) What value or values of x correspond to points of stable equilibrium? (g) Of unstable equilibrium? ed
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