Cannon
Mass - M
Marble
Mass m
Note: Figure not drawn to scale.
Students launch identical marbles of mass mm horizontally from a toy cannon of mass MC,
where Mc > mm, as shown above. The cannon can be adjusted to change the launch speed v of
the marble relative to the ground. Each time a marble is launched, the cannon slides backward
before coming to rest. The coefficient of kinetic friction between the cannon and the ground is u
(mu). For each launch, the students vary the launch speed v and record the distance x the cannon
slides backward for each launch speed.

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 [tex]\rho[/tex] is the momentum of the cannon with mass [tex]M_C[/tex]

The kinetic energy of the canon will be:

[tex]\frac{\rho ^2 }{2 M_C}[/tex]

Also the frictional force acting on the cannon is :

[tex]f = \mu mg[/tex]

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;

[tex]fx = K.E[/tex]

[tex]fx = \frac{\rho ^2 }{2 M_C}[/tex]

[tex]\mu mg x = \frac{\rho ^2 }{2 M_C}[/tex]

[tex]x = \frac{\rho ^2 }{2 \mu mg M_C}[/tex]

[tex]x = \frac{m_m^2 V^2 }{2 \mu mg M_C}[/tex]

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

priyankatutor priyankatutor · Answer 2 · 2021-11-22T08:42:27+01:00

The increase in the mass of the marble increase the distance of the cannon.

Momentum:

Momentum of an object is equal to the product of the mass and the velocity of the object.

The kinetic energy of the cannon

[tex]K_C = \dfrac {\rho^2}{2 M_C}[/tex]

Where,

[tex]\bold{\rho}[/tex] - momentum of the cannon

Mc - mass

The frictional force on cannon

[tex]\bold{F_f = \mu mg}[/tex]

Cannon move a distance x,

Hence,

[tex]\bold {F_f \times x = K_C}\\\\\bold {\mu m g \times x = \dfrac {\rho^2}{2 M_C }}\\\\\bold {x = \dfrac {\rho^2}{2\mu m g M_C }} }\\\\\bold {x = \dfrac {m^2 V^2}{2\mu m g M_C } }[/tex]

Therefore, The increase in the mass of the marble increase the distance of the cannon.

To know more about kinetic energy,

https://brainly.com/question/1266955