Question
Question: A disc of mass 1.0kg is kept floating horizontally in air by firing bullets of mass 0.05kg each vert...
A disc of mass 1.0kg is kept floating horizontally in air by firing bullets of mass 0.05kg each vertically at it, at the rate of 10 per second. If the bullets rebound with the same speed, the speed with which these are fired will be
Solution
Here the disc is floating in air by firing bullets that means the disc is having the downward gravitational pull and a force due to change in momentum of the bullets as shown in the diagram. To get the speed of bullets we can balance the force experienced by the disc. Bullets rebound means they reflect back with the same speed.
Formula used:
F=mdtdv
Complete answer:
From the given figure, we can see that there is an upward force due to the firing of bullets that is a change in momentum of the bullet. The velocity of the bullet is v and the rebounding velocity will be –v. There is also downward force gravitational force shown as Mg.
Now the upward force can be given by the Newton’s second law
F=mdtdv
Where m is the mass of the bullet and change in velocity is given as
dv=v1−v2
v1 is the velocity with which the bullet is fired and v2 is the rebounding velocity. As per question
v1=v and v2=−v
Substituting values we get