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Q07.Conservation of Energy

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1.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 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: m/s m/s m/s m/s

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2.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 As the block goes 2.0 m down the plane, the mechanical energy of the Earth-block system changes by: –9.8 J J 4. –4.6 J J

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25 2.2 kg = 0.25

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3.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 v 2 4. m v 2 / 4k 5.

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4.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: J J J J J

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10 m 2 m

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5.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: m/s m/s m/s m/s m/s

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5cm1cm

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6.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? 1. m g / 2 2. m g 3. 2 m g 4. 3 m g 5. m g r

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mg T

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6.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 ? 1. R /4 2. R /2 3. R 4. 2 R 5. zero

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7.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:

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At top, T = 0 : E Conservation :

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8.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: 1. its mechanical energy is a minimum 2. the forces on it are balanced 3. it is not accelerating 4. its speed is a minimum 5. it experiences a net upward force

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1. its mechanical energy is a minimum 2. the forces on it are balanced 3. it is not accelerating 4. its speed is a minimum 5. it experiences a net upward force

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