The force required to compress a non-standard spring varies as the spring is com

Question

The force required to compress a non-standard spring varies as the spring is compressed, as shown by the plot of force vs displacement in the figure. The distances in the figure are x_1= 15 cm, x_2= 25 cm, x_3=55 cm, x_4=75 cm, and the forces are F_1= 110 N and F_2=65 N. Write an equation, in terms of the variables in the problem statement, for the amount of work required to compress the spring from the origin to x_4. Calculate the work done, in joules, on the spring as it is compressed from the origin to point x_4. Write an equation, in terms of the variables in the problem statement, for the amount of work required to compress the spring from x_1 to x_3. Calculate the work done, in joules, on the spring it is compressed from the point x_1 to the point x_3.

Explanation / Answer

A)

F1 = 110, F2 = 65N

x1 = 0.15 m; x2 = 0.25m; x3 = 0.55m; x4 = 0.75m

Work done would be area under the graph with sign:

Wnet = 1/2*F1*x2 -1/2*F2*(x4-x2)

Part B)

Wnet = 1/2*F1*x2 -1/2*F2*(x4-x2)

= 0.5*110*0.25 - 0.5*65*0.2

= 13.685 Joules

Part C

W = 0.5x(x2-x1)xF1 - [0.5x(x3-x2)xF2]

Part D

W = 0.5x(x2-x1)xF1 - [0.5x(x3-x2)xF2]

= 0.5x0.10x110 - [0.5x0.3x65]

= - 4.25 Joules

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