Question

A glider with mass m = 0.8 kg sits on a frictionless air track. It is connected to a massless spring with force constant k = 30 N/m. The glider is initially at x=0, and the spring is relaxed. You then hit the glider with a hammer, which gives it an initial velocity of υ0 = 8 m/s in the positive x direction. At what x positions will the speed of the glider be zero?

Answer 1

The position is

`d_(o)=1.706m`

Step-by-step explanation:

The kinetic energy of the motion is

`E_(K)=(1)/(2)*m*v^2`

`E_(K)=(1)/(2)*0.8kg*8((m)/(s))^2`

`E_(K)=25.6 J`

So apply the conservation of energy the force of the spring is the same of the kinetic energy

`F_(s)=(1)/(2)*k*d^2`

`F_(s)=E_(K)`

`25.6=(1)/(2)*30(N)/(m)*d_(o)^2`

Solve to do

`d_(o)=\sqrt{(2*25.6J)/(30(N)/(m))}`

`d_(o)=1.706m`