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# kinetic energy and potenital energy

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26. 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:

27. A small object of mass m, on the end of a light cord, is held horizontally at a distance r from a fixed support shown. The object is then released. What is the tension in the cord when the object is at the lowest pont of its swing?

28. A block is released from rest at point P and slides along the frictionless track shown. At point Q, its speed is:

29. A rectangular block is moving along a frictionless path when it encounters the circular loop as shown. The block passes point 1, 2, 3, 4, 1 before returning to the horizontal track. At pont 3

30. a particle is release from rest at the point x = a and moves along the x axis subject to the potenital energy function U(x) shown. The particle

31. As a particle moves along the x axis it is acted by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labeled regions according to the magnitude of the forest, least to greates

https://brainmass.com/physics/newtons-second-law/kinetic-energy-potential-energy-86870

#### Solution Preview

26. 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 force 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 :

The potential energy of the spring is , the block's kinetic energy is
The block's initial kinetic energy is
(1)
Since the block's kinetic energy is equal to the potential energy of the spring,

Substitute it to (1)