In a physics lab experiment, a compressed spring launches a 32 g metal ball at a 35 degree angle compressing the spring 18 cm cause the ball to hit the floor 1.6 m below the point at which it leaves the spring after traveling 5.2 m horizontally. what is the spring constant?

The value of spring constant is .

Explanation:

Given: A compressed spring launches a metal ball at a degree angle compressing the spring cause the ball to hit the floor below the point at which it leaves the spring after traveling horizontally.

As mentioned in question:

The ball hits the floor at below the initial position then

And horizontal distance of ball is .

Now, velocity in both directions are .

Then, and

Net velocity

Using Energy conservation:

Hence, The value of spring constant is .

Learn more about Energy conservation law here:

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Ball hits the floor at 1.6 m below the initial position

So here we can say that

also it will hit at horizontal distance of 5.2 m

let say its velocity in x and y directions are given as

now we can say

from above two equations

as we know that it is projected at an angle of 35 degree

so we know that

now we have

also we can find vertical component of velocity as

now we will find net velocity as

now by energy conservation we can say

so spring constant is 37.2 N/m