Consider the following experiment. You have an ideal (massless) spring with spri

Question

Consider the following experiment. You have an ideal (massless) spring with spring constant k = 50 N/m resting on a frictionless slope of angle ? = 30 degrees. Define your coordinate axis, x, as shown with x positive upwards and x = 0 as the point where the spring is not stretched or compressed. You place an object of mass M = 5.0 kg on the slope, attach it to the spring, and slowly lower it to the point xi, where it will be at rest (stationary) with just the spring, gravitational, and normal forces acting on it. The object is connected to the spring and not moving. You then give the object a very quick impulse so that it has a velocity vi = 5.0 m/s down the slope. The impulse is short enough that you take the initial position to be xi and the initial velocity to be vi. If the object remains attached to the spring, what is the maximum distance, xf, that the mass goes up the slope?

Explanation / Answer

it undergoes simple harmonic motion

in SHM we have

Vmax = Aw

w = sqrt ( k/m)

Vmax = 5m/sec

A = 1.5811m

we know that

xi = mgsin 30 /k

xi = 0.49m

xi +xf = A

xf = A-xi

xf = 1.0911 m

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