Question

Cannon

Answer 1

Answer:

the distance x increases as the student increase the mass of the cannon.

Explanation:

a) From the question ; we get to understand that for each launch, the students use a different mass which is launch at  speed v relative to the ground.

This changes in the mass used brought about a change in the momentum at the same speed v ; perhaps an increase in momentum. However; since the conservation of the momentum is considered at each launching.

The momentum of the marble = momentum of the cannon

But since the momentum of the cannon increase ; therefore the same equivalent changes takes place in its kinetic energy . Therefore , the kinetic energy will increase and the distance will also increase in the bid to quench the amount of energy generated. Thus, the distance x increases as the student increase the mass of the cannon.

b)We all know that  conservation of the momentum will definitely  takes place after launching of the cannon.

Let assume that $\rho$ is the momentum of the cannon with mass $M_C$

The kinetic energy of the canon will be:

$\frac{\rho ^2 }{2 M_C}$

Also the frictional force acting on the cannon is :

$f = \mu mg$

If the cannon move at an  additional distance x; the frictional force acting at this area quench the amount of the energy generated and consume the kinetic energy of the cannon;

So;

$fx = K.E$

$fx = \frac{\rho ^2 }{2 M_C}$

$\mu mg x = \frac{\rho ^2 }{2 M_C}$

$x = \frac{\rho ^2 }{2 \mu mg M_C}$

$x = \frac{m_m^2 V^2 }{2 \mu mg M_C}$

Thus; it is consistent with the answer in (a) as increase in the mass of the marble will bring about an increase in distance x