Question

A spring with spring constant k is positioned vertically and then compressed from its equilibrium length by a distance Delta y (Figure 1). A ball of mass m is placed on top of the spring, and is launched into the air when the spring is released (this setup is similar to the projectile launcher seen earlier in the semester). The ball travels to a maximum height h_max. Using the Work-Kinetic Energy theorem, determine h_max in terms of the given variables and any other constants you deem necessary. If you use the variable Delta y, put it in parentheses Using the Work-Kinetic Energy theorem, write an expression for the speed of the ball v at y = 0 in terms of the given variables and any other constants you deem necessary. If you use the variable Delta y, put it in parentheses.

Answer 1

Theorem of work and energy says:
the sum of all jobs acting on a body is equal to the kinetic energy vaciacion experiencing

the reference is considered lower

Part A

The forces that do work on the ball are:
work done by the weight.

where:

mass ball

acceleration of gravity

variation of height

Finally

organizing

Work done by the spring force

the net work on the ball is

but also net work is equal to the change in kinetic energy

It is zero. at the bottom starts from rest at the top and stays momentarily at rest

expression for

finally

part B

It applies the theorem of work and energy again.
In this case the

The forces that do work on the ball are:
work done by the weight.

where:

mass ball

acceleration of gravity

variation of height

Finally

Work done by the spring force

the net work on the ball is

but also net work is equal to the change in kinetic energy

the velocity is zero at the start

now

expression for the velocity

simplifying