physics - question

Question

In a physics lab experiment, a spring clamped to the table shoots a 20 g ball horizontally. When the spring is compressed 18 cm , the ball travels horizontally 5.2 m and lands on the floor 1.6 m below the point at which it left the spring.

what is the spring constant?

Answer 1

There are two parts to the problem. In the first part, the ball goes from spring energy to kinetic energy. In the second part, we have a horizontal launch problem with the typical variables of v, h, R, and t_air .

For horizontal launches, if you know 2/3 of v, R, or h , you can solve for the third. You do this by using the two equations of motion in y and x:

x = vt (constant velocity - true for any t)

y = 1/2 gt² (constant a=g true for any t)

the usual procedure is to solve for t_a:and find the last unknown (In this case given R and h, find v and t_a

R = vt_a and h = 1/2 gt_a² therefore t_a= sqrt(2h/g) and v = R/t_a (plug in values)

Now, we can set up the energy balance:

E_spr,initial = E_K,final or 1/2 kx² = 1/2 mv²

solving for k: k = mv²/x² (We are given x and m; v is the answer to "second part)

Note: you will get N/m for k if you put m in kg and x in m only!!! Leaving these as g and cm will produce nonsense.