Mechanics Paper 4 June 2010

Four coplanar forces act at the point O, as shown in the diagram. A force of 2N acts along the positive y-axis. A force of 3N acts at 30 degrees to the left of the positive y-axis. A force of 5N acts at 30 degrees to the right of the positive y-axis. A fourth force of 2N acts at right angles to the 5N force, below the positive x-axis. The forces $\mathbf{i}$ and $\mathbf{j}$ are of 1N magnitude in the directions of the x and y axes respectively.

The resultant of the four forces is $a\mathbf{i}+b\mathbf{j}$.

Find the value of b.

Four coplanar forces act at the point O, as shown in the diagram. A force of 2N acts along the positive y-axis. A force of 3N acts at 30 degrees to the left of the positive y-axis. A force of 5N acts at 30 degrees to the right of the positive y-axis. A fourth force of 2N acts at right angles to the 5N force, below the positive x-axis. The forces $\mathbf{i}$ and $\mathbf{j}$ are of 1N magnitude in the directions of the x and y axes respectively.

The resultant of the four forces is $a\mathbf{i}+b\mathbf{j}$.

Find the value of a.

Particles A and B are connected by a light inextensible string which passes over a smooth, light fixed pulley. Particle A has mass 2 kg and particle B has mass 5 kg. The two particles are released from rest with the string taut.

Find, in terms of g, the acceleration of this system.

Particles A and B are connected by a light inextensible string which passes over a smooth, light fixed pulley. Particle A has mass 2 kg and particle B has mass 5 kg, and they are released from rest with the string taut. At the same instant a third particle C is released from rest 14 m above the horizontal ground and falls freely. Particle B and particle C reach the ground at the same time.

Find the time taken for the particles to reach the ground.

Particles A and B are connected by a light inextensible string which passes over a smooth, light fixed pulley. Particle A has mass 2 kg and particle B has mass 5 kg, and they are released from rest with the string taut. At the same instant a third particle C is released from rest 14 m above the horizontal ground and falls freely. Particle B and particle C reach the ground at the same time.

Find the initial vertical distance of B above the ground.

A parcel of mass 5 kg is released from rest on a rough ramp of inclination $\theta=\sin^{-1}\left(\frac{3}{5}\right)$ and slides down the ramp.

Find the reactional force, R, in terms of g.

A parcel of mass 5 kg is released from rest on a rough ramp and slides down it. After 3 seconds the parcel has a speed of 4,9 m/s.

Find the acceleration of the parcel down the ramp.

An archer shoots an arrow from a point 1.5 m above level ground, at an angle 30 degrees above the horizontal. The speed of projection is 20 ms$^{-1}$. The arrow strikes a tree which is 30 m horizontally from the point where the archer is standing.

Find the time taken for the arrow to reach the tree.

An archer shoots an arrow from a point 1.5 m above level ground, at an angle 30 degrees above the horizontal. The speed of projection is 20 ms$^{-1}$. The arrow strikes a tree which is 30 m horizontally from the point where the archer is standing.

Calculate the magnitude of the velocity of the arrow when it strikes the tree.

An archer shoots an arrow from a point 1.5 m above level ground, at an angle 30 degrees above the horizontal. The speed of projection is 20 ms$^{-1}$. The arrow strikes a tree which is 30 m horizontally from the point where the archer is standing.

Calculate the angle, in degrees below the horizontal, at which the arrow is travelling when it strikes the tree.