Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 1: CROSS-TOPIC REVIEW EXERCISE 1

A force $F$ acts in a horizontal plane and has components $25 \mathrm{N}$ in the $x$ -direction and $-17 \mathrm{N}$ in the $y$ -direction relative to a set of axes. The force acts at an angle $\alpha$ below the $x$ -axis.

Find the sizes of $F$ and $\alpha .$

The graph shows the velocity of a parachutist as she falls from an aircraft until she hits the ground $50 \mathrm{s}$ later.

There are four stages to the motion: falling freely under gravity with the parachute closed; decelerating with the parachute open; falling at constant speed with the parachute open; and coming to rest instantaneously on hitting the ground.

Find the total distance fallen.

The graph shows the velocity of a parachutist as she falls from an aircraft until she hits the ground $50 \mathrm{s}$ later.

There are four stages to the motion: falling freely under gravity with the parachute closed; decelerating with the parachute open; falling at constant speed with the parachute open; and coming to rest instantaneously on hitting the ground.

The parachutist has mass $70 \mathrm{kg}.$ Show that the upward force on the parachutist due to the parachute during the second stage is $1148 \mathrm{N}.$

A particle of mass $6.3 \mathrm{kg}$ is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point $X.$ It is held in equilibrium by a horizontal force $F$ when the string is at an angle $\alpha$ to the vertical, where $\tan \alpha =\frac{20}{21}.$ Find the tension in the string and the size of $F.$

Two forces, each of size $8 \mathrm{N},$ have a resultant of $13 \mathrm{N}.$
Find the angle between the forces.

Two forces, each of size $8 \mathrm{N},$ have a resultant of $13 \mathrm{N}.$
The two given forces of magnitude $8 \mathrm{N}$ act on a particle of mass $m \mathrm{kg},$ which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has magnitude $7 \mathrm{N}.$ Find $m$ and the acute angle that one of the $8 \mathrm{N}$ forces makes with the surface.

A particle $P$ is in equilibrium on a smooth horizontal table under the action of four horizontal forces of magnitudes $6 \mathrm{N}, 5 \mathrm{N}, F \mathrm{N}$ and $F \mathrm{N}$ acting in the directions shown. Find the values of $\alpha$ and $F.$

A particle $P$ of weight $21 \mathrm{N}$ is attached to one end of each of two light inextensible strings, $S_1$ and $S_2,$ of lengths $0.52 \mathrm{m}$ and $0.25 \mathrm{m}$ respectively. The other end of $S_1$ is attached to a fixed point $A,$ and the other end of $S_2$ is attached to a fixed point $B$ at the same horizontal level as $A.$ The particle $P$ hangs in equilibrium at a point $0.2 \mathrm{m}$ below the level of $AB$ with both strings taut (see diagram). Find the tension in $S_1$ and the tension in $S_2.$