Mechanics questions | form five Physics

In the first second of its flight a rocket ejects 1/60 of its mass with a relative velocity of
2400m/s.

1. Find its acceleration.
2. What is the final velocity if the ratio of initial to final mass of the rocket is 4 at a time of 60 seconds?

A ball is thrown upwards with an initial velocity of 33m/s from a point 65° on the side of a hill which slopes upward uniformly at an angle of 28°.

1. At what distance up the slope does the ball strike?
2. Calculate the time of flight of the ball.

1. State the principle of conservation of linear momentum.
2. Give two examples of the principle stated in (i).

A cannon of mass 1300kg fires a 72kg ball in a horizontal direction with a muzzle speed of 55m/s. If the cannon is mounted so that it can recoil freely calculate the:

1. recoil velocity of the cannon relative to the earth.
2. horizontal velocity of the ball relative to the earth.

1. Define the term ‘radial acceleration’.
2. An insect is released from rest at the top of the smooth bowling ball such that it slides over the ball. Prove that it will lose its footing with the ball at an angle of about 48° with the vertical.

1. State where the magnitude of acceleration is greatest in a simple harmonic motion (S.H.M.)?
2. Sketch a graph of acceleration against displacement for a simple harmonic motion.

A vertical spring fixed at one end has a mass of 0.2kg and is attached at the other end.
Determine the:

1. Extension of the spring.
2. Energy stored in the spring.

The displacement of a particle from the equilibrium position moving with simple harmonic motion is given by ​ x = 0.05 sin 6​t ​ , where t is time in seconds measured from an instant when x ​ = 0. Calculate the:

1. Amplitude of oscillations.
2. Period of oscillations.
3. Maximum acceleration of the particle.

1. Define the universal gravitational constant.
2. How is gravitational potential related to gravitational field strength?

1. Write down an expression for the acceleration due to gravity (g) of a body of mass ​ m which is at a distance ​ r ​ from the centre of the earth.
2. If the earth were made of lead of relative density of 11.3, what would be the value of acceleration due to gravity on the surface of the earth?