The block in the figure below lies on a horizontal frictionless surface and is a

Question

The block in the figure below lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 57 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 2.6 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. Assume that the stopping point is reached. (a) What is the position of the block? Incorrect: Your answer is incorrect. m (b) What is the work that has been done on the block by the applied force? J (c) What is the work that has been done on the block by the spring force? J During the block's displacement, find the following values. (d) The block's position when its kinetic energy is maximum. m (e) The value of that maximum kinetic energy. mJ

Explanation / Answer

a)

let the spring is stretched by "x" when the block stops

W + (0.5) k x2 = 0

- F x + (0.5) k x2 = 0

F = (0.5) k x

inserting the values

2.6 = (0.5) (57) x

x = 0.091 m

b)

W = Fx

W = 2.6 x 0.091

W = 0.24 J

c)

work done by spring = - W = - 0.24 J

d)

kinetic energy is maximum when velocity is maximum and velocity is maximum when the acceleration becomes 0 or

net force = 0

F - kx = 0

F = k x

2.6 = 57 x

x = 0.046 m

2.6 = 57 x

x = 0.046 m

b)

work done = spring potential energy gained

W = (0.5) k x2 = (0.5) (57) (0.046)2 = 0.0603 J

c)

work done by spring on block = 0.0603 J

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