QUESTION $5$

A$.$ Using eirher words or an equation, state the Principle of Conservation of Energy

B$.$ Construction is going on all the time at Stockton. During this construction a big stone of mass $20$ kg drops $($starting from rest$)$ from a roof $5$ meters, above ground level. There is NO friction. With what speed will the stone hit the ground $($Hint: use the Principle of Conservation of Energy$)?$

C$.$ A diver of mass $40$ kg drops $($starting from rest$)$ from a diving board $20$ meters above the water $($which is at ground level$).$ As she is falling through the air there is a constant upward frictional force of $100$ newtions acting on her, opposing the motion during the entire fall.

a$.$ Calculate the work done by the frictional force while the diver falls the distance of $20$ meters.

b$.$ Assume that this work generates an equal amount of heat energy in Joules. What is this amount of heat energy, in joules. Just use the value you found in part a above

c$.$ Now use the Principle of Conservation of Energy $($including heat energy$)$ to calculate the speed with which the diver will hit the water. Remember that the diver dropped from a height of $20$ meters to the water at ground level.

D$.$ When a force of $10$ newtons is applied to a given spring it stretches by $5$ meters from its $.$ equilibrium position. The spring is always horizontal.

a$.$ Find the spring constant $k$ of the spring.

b$.$ Find the potential energy that is stored in the spring when it is stretched, as noted above, by $5$ meters from its equilibrium position.

c$.$ By how much would this unextended spring stretch if a force of $24$ newtons is applied to it$?$

E$.$ A certain motor is rated at $2$ horsepower.

a$.$ What is the motor's rating in Watts?

b$.$ How much work in Joules $($or Newton e meters$)$ would this motor do in $3$ seconds?

c$.$ How long would it take this motor to do $3730$ joules of work?A