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/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: 2.5 m/s 5.7 m/s 7.9 m/s 11 m/s <PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>



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: –9.8 J 9.8 J –4.6 J 4.6 J <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

 = 0.25 2.2 kg 25

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 <PowerClick><Answer>1</Answer><Option>5</Option></PowerClick>

A 700-N man jumps out of a window into a fire net 10 m below 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 <PowerClick><Answer>5</Answer><Option>5</Option></PowerClick>

10 m 2 m

A toy cork gun contains a spring whose spring constant is 10. 0 N/m 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 <PowerClick><Answer>3</Answer><Option>5</Option></PowerClick>

5cm 1cm

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 <PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

T mg 

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 <PowerClick><Answer>2</Answer><Option>5</Option></PowerClick>

 

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: <PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

At top, T = 0 :  E Conservation : 

its mechanical energy is a minimum the forces on it are balanced 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 <PowerClick><Answer>4</Answer><Option>5</Option></PowerClick>

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