Aspring of spring constant k = 340 nm-1 is used to launch a 1.5-kg block along a horizontal surface by compressing the spring by a distance of 18 cm. if the coefficient of sliding friction between the block and the surface is 0.25, how far does the block slide?

The block slides 1.5m

Explanation:

To solve this problem we need the concepts relate to work energy, work done, frictional force and normal force.

We know for definition that,

Where W is the work and \Delta KE the change in Kinetic Energy, F the force and d the distance.

The expression is relate to the Hook's law where F=kx, being k the elastic constant and x the displacement of the object.

We know as well that Frictional Force is given by

Where is the coefficient of friction, m the mass and g the gravity acceleration.

We can now solve the problem. Using the first equation we have,

Using the second form for work,

Here we know that is zero and F_f is equal to mg

Re-arrange for d,

Replacing the values we have,

The block slides 1.5m

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the area between the graph and the t axis