# A Discussion On Compressed Springs And Spring Constants

In a physics lab experiment, a compressed spring launches a 22g metal ball at a 35 degree angle. Compressing the spring 19cm causes the ball to hit the floor 2.0m below the point at which it leaves the spring after traveling 5.4m horizontally.

What is the spring constant?

k = __________________ N/m

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Spring Question-Compressed Spring

In a physics lab experiment, a compressed spring launches a 22g metal ball at a 35 degree angle. Compressing the spring 19cm causes the ball to hit the floor 2.0m below the point at which it leaves the spring after traveling 5.4m horizontally.

What is the spring constant?

k = __________________ N/m

Let the spring constant be K and the velocity of the ball just after it released is v.

As the elastic potential energy stored in the spring compressed by L is given by

U = ½ K L2

Using law of conservation of mechanical energy the velocity of projection v is given by

Gain in kinetic energy = loss in elastic potential energy

Or

Or --------------------- (1)

Now for a projectile motion using the equation of trajectory (point of projection as origin and upward direction positive) is written as

Here is the angle of projection and (x, y) is the coordinates of any point on the trajectory.

Now in our case as (x, y) = (5.4 m, - 2.0 m) and = 35 deg, substituting in above equation of trajectory we get

Or

Or

Gives

Substituting this in equation (1) with other values we get

Or

Thus the spring constant of the spring is 22 N/m.

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