A spring whose spring constant is 850 N/m is compressed 0.40 m.  What is the maximum speed it can give to a 500. g ball? 4.    If the spring in #3 were compressed twice as much, how many times greater would the velocity of the ball be?

part 1. 1/2kx^2 = 1/2mv^2

1/2(850)(0.40)^2 = 1/2(0.5)v^2

68 = 0.25v^2

272 = v^2

v = 15.49m/s

Explanation:

part 1. the max potential energy would be equal to the maximum kinetic energy assuming no energy is lost, because of this, we can set the spring potential energy to the kinetic energy. from there plug in all the variables sorry all known variables and solve for v. make sure to plug in 0.5 for mass so that it is in kilograms.  

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.