State the principle of conservation of momentum and state the condition under which it is valid.

 

 An arrow of mass $0.25 \mathrm{kg}$ is fired horizontally towards an apple of mass $0.10 \mathrm{kg}$ that is hanging on a string, as shown in Figure. The horizontal velocity of the arrow as it enters the apple is $30 \mathrm{m}{ \mathrm{s}}^{-1}$. The apple was initially at rest and the arrow sticks in the apple. Calculate the horizontal velocity of the apple and arrow immediately after the impact.

 An arrow of mass $0.25 \mathrm{kg}$ is fired horizontally towards an apple of mass $0.10 \mathrm{kg}$ that is hanging on a string, as shown in Figure. The horizontal velocity of the arrow as it enters the apple is $30 \mathrm{m}{ \mathrm{s}}^{-1}$. The apple was initially at rest and the arrow sticks in the apple.Calculate the change in momentum of the arrow during the impact.

b An arrow of mass $0.25 \mathrm{kg}$ is fired horizontally towards an apple of mass $0.10 \mathrm{kg}$ that is hanging on a string, as shown in Figure. The horizontal velocity of the arrow as it enters the apple is $30 \mathrm{m}{ \mathrm{s}}^{-1}$. The apple was initially at rest and the arrow sticks in the apple.Calculate the change in total kinetic energy of the arrow and apple during the impact.

b An arrow of mass $0.25 \mathrm{kg}$ is fired horizontally towards an apple of mass $0.10 \mathrm{kg}$ that is hanging on a string, as shown in Figure. The horizontal velocity of the arrow as it enters the apple is $30 \mathrm{m}{ \mathrm{s}}^{-1}$. The apple was initially at rest and the arrow sticks in the apple.

(iv) A rubber-tipped arrow of mass $0.25 \mathrm{kg}$ is fired at the centre of a stationary ball of mass $0.25 \mathrm{kg}$. The collision is perfectly elastic. Describe what happens and state the relative speed of separation of the arrow and the ball.

State what is meant by a perfectly elastic collision.

State what is meant by:

(ii) A completely inelastic collision.

(b) A stationary uranium nucleus disintegrates, emitting an alpha-particle of mass $6.65\times {10}^{-27} \mathrm{kg}$ and another nucleus $\mathrm{X}$ of mass $3.89\times {10}^{-25} \mathrm{kg}$.

(i) Explain why the alpha-particle and nucleus $X$ must be emitted in exactly opposite directions.

A stationary uranium nucleus disintegrates, emitting an alpha-particle of mass $6.65\times {10}^{-27} \mathrm{kg}$ and another nucleus $\mathrm{X}$ of mass $3.89\times {10}^{-25} \mathrm{kg}$.

Using the symbols $v_{\alpha }$ and $v_x$ For velocities, write an equation for the conservation of momentum in this disintegration.