Assume that the magnitude of the force applied by the spring is of the form F(x)

Question

Assume that the magnitude of the force applied by the spring is of the form F(x)=Ax2.

a) Which quantities should be graphed in order to produce a graph with a straight line whose slope could be used to calculate a numerical value for A? Explain why.

b) Calculate values for any of the quantities identified in (a) that are not given in the data, and record these values in the table above. Label the top of the column, including units.

c) Using a straight edge, plot the quantities you indicated in (a). Label the axes with the variables and appropriate numbers to indicate the scale.

d) Using your graph, calculate A.

The spring is then placed horizontally on the floor. One end of the spring is fixed to a wall. A cart of mass 0.50kg moves on the floor with negligible friction and collides head on with the free end of the spring, compressing it a maximum distance of 0.10m.

e) Calculate the work done by the cart in compressing the spring 0.10m from its equilibrium length.

f) Calculate the speed of the cart just before it strikes the spring.

Explanation / Answer

For part a), slope = rise/run. Since y=Ax2, you should have the x-axis as x2 and y-axis as F to give you slope = A = y/x2.

For part b), you should write out the values of x2 in the 3rd column

For part c) and d), draw a cartesian plane, label both x- and y-axis, plot the values of x2 and their respective F value

Good luck on part e) and f)

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