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 35 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 3.3 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.

What is the position of the block?
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)The stopping condition is

W=F*x=1/2k*x^2

x=2F/k = 0.188571 m

b)

W=F*x=2*F^2/k = 0.6222857143 J

c)The work done by the block on the spring force must be exactly the same to conserve energy

W= 0.6222857143 J

d) The kinetic energy change of the block will be the difference between the work done by the force and thespring’s potential energy

K=WUspring=F*x1/2*k*x^2

The maximum kinetic energy is when dK/dx= 0

dK/dx=Fk*x= 0

xmax K=F/k = 0.09428571429 m

e) The maximum kinetic energy is when there is no net force on the block

Kmax=F*x1/2*k*x^2=F^2/2*k= 155.5714286 mJ

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