Tutorial $6-$ Work, Power & Energy

NB: Please underline and Highlight all Final Answers

Question $1$

A force of $60$ N is required to compress a spring for a distance of $25$ mm $.$ If this spring is placed on the floor in a vertical position, and compressed by an amount of $140$ mm $,$ how high could it shoot a $5$ kg ball.

Question $2$

$2\mathrm{.}1$ A $10$ tonne truck drives up an incline of $1$ in $100.$ The power that the engine develops is $60$ kW and the tractive resistance of the truck is $520$ N $.$ Calculate the maximum velocity $($in $k\frac{m}{h})$ at which the truck can travel up the incline.

$2\mathrm{.}2$ The truck now drives up the same hill at a velocity of $80k\frac{m}{h}.$ At a certain point $A,2km$ from the top of the hill, the driver de$-$clutches and free wheels up the hill. Will the truck be able to make it to the top of the hill before it stops and starts rolling back? Justify your answer with appropriate calculations.

Question $3$

A $3-$tonne truck travelling at a velocity of $72k\frac{m}{h}$ free$-$wheels for $1,5km$ down a hill from point $A$ to point $B$ as shown. The tractive resistance of the truck is $120\frac{N}{?}$ tonne. The truck then travels $1$ km along the level ground from B to C while still free$-$wheeling and comes to a slope of $1$ in $200$ at $C$ as shown. How many kilometers up along the slope to D $,($ie: $skm)$ will the truck be able to travel before coming to a stop?