Question

A spring whose constant is 850N/m is compressed 0.40 m. (Ignore friction)

A. What is the maximum speed it can give to a 500 g ball when shot horizontally?

B. If the spring were compressed twine as much, (0.80 m)
I) write the expression (math model) for velocity in terms of the variable
ii) how many times greater did the velocity of the ball be?

(Create an LOL chart)

Answer 1

hint:
if I call with \(\Delta \) the compression of the spring, then the potential energy \(PE\)of such spring, is:
\[\Large PE = \frac{1}{2}k{\Delta ^2}\]
where \(k=850\)
the kinetic energy of the ball, is:
\[\Large KE = \frac{1}{2}m{v^2} = PE\]
therefore:
\[\Large \frac{1}{2}m{v^2} = \frac{1}{2}k{\Delta ^2} \Rightarrow v = ...?\]
if the new compression \(\Delta'=2\Delta\) is twice of the old one, then the new kinetic energy will be this:
\[\Large \frac{1}{2}m{v_1}^2 = \frac{1}{2}k{\left( {2\Delta } \right)^2}\]
therefore, we have:

\[\Large \frac{1}{2}m{v_1}^2 = 2k{\Delta ^2} \Rightarrow {v_1} = ...?\]