Finding the Spring Constant of a ball

[ckrup]

1. A spring clamped to a table shoots a 20 g ball horizontally. When the spring is compressed 18 cm the ball travels horizontally 5.1 m and lands on the floor 1.7 m below the point at which it left the spring. What is the spring constant (in N/m)

2. I tried using k=mg/x (x being distance of the spring compression) but am at a COMPLETE loss as how to solve it!

 

[LowlyPion]

1. A spring clamped to a table shoots a 20 g ball horizontally. When the spring is compressed 18 cm the ball travels horizontally 5.1 m and lands on the floor 1.7 m below the point at which it left the spring. What is the spring constant (in N/m)

2. I tried using k=mg/x (x being distance of the spring compression) but am at a COMPLETE loss as how to solve it!

Welcome to PF.

This is a double problem.

First find the initial velocity, which is totally in the x direction.

You do that by figuring the time for it to drop 1.7 m.

Take that time and determine horizontal velocity by 5.1 m / Time to drop.

Now for part 2:
You know the V so you know KE which is mV²/2

If you know KE then you know how much PE was initrially in the spring by PE = k*x²/2

You know x, you know PE now you can finally know k.

 

[ineedhelp1]

i have a similar problem to this one and am stuck. Isn't the ball moving in the y direction also since it falls below where it left the spring?

 

[LowlyPion]

i have a similar problem to this one and am stuck. Isn't the ball moving in the y direction also since it falls below where it left the spring?

Welcome to PF.

Yes. Gravity does develop a y component of velocity. But the x component only is the initial velocity and it is this velocity that determines how far from the table it lands.

The Vx * t is that distance. Hence the importance of calculating the t in order to determine that distance.