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Q07. Conservation of Energy

Q07. Conservation of Energy. A 0.20- kg particle moves along the x -axis under the influence of a stationary object. The potential energy is given by : U ( x ) = (8.0 J / m 2 ) x 2 + (2.0 J / m 4 ) x 4

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Q07. Conservation of Energy

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  1. Q07. Conservation of Energy

  2. A 0.20-kg particle moves along the x-axis under the influence of a stationary object. The potential energy is given by : • U(x) = (8.0 J/m2) x2 + (2.0 J/m4) x4 • where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is: • 0 • 2.5 m/s • 5.7 m/s • 7.9 m/s • 11 m/s

  4. A 2.2-kg block starts from rest on a rough inclined plane that makes an angle of 25° with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by: • 0 • –9.8 J • 9.8 J • –4.6 J • 4.6 J

  5.  = 0.25 2.2 kg 25

  6. A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of: • (1/4) m v2 • m v2 / 4k

  7. A 700-N man jumps out of a window into a fire net 10 m below. The net stretches 2 m before bringing the man to rest and tossing him back into the air. The maximum potential energy of the net, compared to it's unstretched potential energy, is: • 300 J • 710 J • 850 J • 7000 J • 8400 J

  8. 10 m 2 m

  9. A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is: • 6.32 m/s • 1.63 m/s • 2.00 m/s • 2.08 m/s • 2.45 m/s

  10. 5cm 1cm

  11. A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support as shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its swing? • m g / 2 • m g • 2 m g • 3 m g • m g r

  12. T mg 

  13. A small object of mass m starts at rest at the position shown and slides along the frictionless loop-the-loop track of radius R. What is the smallest value of y such that the object will slide without losing contact with the track ? • R /4 • R /2 • R • 2 R • zero

  15. A ball of mass m, at one end of a string of length L, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is:

  16. At top, T = 0 :  E Conservation : 

  17. A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes points 1,2,3,4,1 before returning to the horizontal track. At point 3: • its mechanical energy is a minimum • the forces on it are balanced • it is not accelerating • its speed is a minimum • it experiences a net upward force

  18. its mechanical energy is a minimum the forces on it are balanced it is not accelerating its speed is a minimum it experiences a net upward force

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