A block of mass $m=5kg$ is pushed a distance $d=2\mathrm{.}2m$ up

along the $=30$ frictionless incline. horizontal by a constant

applied force of magnitude $F=160N$ directed at an angle

$=45$ below the horizontal as shown in the figure.

Determine the work done on the block by $($a$)$ the the

horizontal force, $($b$)$ the gravitational force on the block

during this displacement, $($c$)$ the normal force. and $($d$)$ What

is the speed of the block $($assume that it is zero initially$)$ after

this displacement?

A block of mass $8kg$ is released from rest at $A.$ The section $AB$ is one quadrant of a circle

of radius $1\mathrm{.}5m$ and is frictionless. $B$ to $C$ is a horizontal span $6\mathrm{.}00m$ long with a coefficient

of kinetic friction ${}_k=0\mathrm{.}2.$ The section CD under the spring is frictionless. After sliding on

the track, it compresses the spring by $0\mathrm{.}6m.$ Determine: $(a)$ the velocily of the block at

point $B$;$(b)$ the thermal energy produced as the block slides from $B$ to $C$;$(c)$ the velocity

of the block at point $C$; $(d)$ the stiffness constant $k$ for the spring.

A proton collides elastically with another proton that is initially at rest. The incoming

proton has an initial speed of $2\mathrm{.}4{10}^5\frac{m}{s}$ and makes a glancing cullision with the second

proton. After the collision, one proton moves off at an angle of $53$ to the original direction

of motion and the second deflects at an angle of $$ to the same axis. Find the final speeds

of the two protons and the angle $.$