An ice skater of mass (on frictionless ice) fires a bullet of mass 10 grams that leaves the barrel at 500 m/s (in the x-direction relative to the ground)
A) what is the recoil velocity of the skater relative to the ground?
B) how much work is done in the bullet by the exploding gunpowder?
A) this is conservation of momentum, which is zero in both cases. Unfortunately you neglected to give the skater's mass.
mv (skater) = mv (bullet)
watch units.
B) W = KE of bullet = 1/2(.001)500^2
To find the answers to these questions, we can use the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant before and after an event, as long as no external forces are acting on it.
A) To find the recoil velocity of the skater relative to the ground, we can consider the system to be the skater and the bullet together. Initially, both the skater and the bullet are at rest, so the initial momentum of the system is zero. After the bullet is fired, the skater and the bullet will move in opposite directions.
According to the conservation of momentum, the final momentum of the system is also zero. The momentum of an object is given by the product of its mass and velocity.
Let's assume the recoil velocity of the skater is v. The mass of the skater is M, and the mass of the bullet is m. The velocity of the bullet relative to the ground is v_bullet.
The momentum after the bullet is fired is given by:
Final momentum = Momentum of the skater + Momentum of the bullet
Since the skater moves in the opposite direction to the bullet, we have:
0 = (M * (-v)) + (m * v_bullet)
Simplifying the equation, we get:
-Mv = mv_bullet
By substituting the given values, we can solve for v, whereby Mass of the skater (M) is needed.
B) To find the work done on the bullet by the exploding gunpowder, we need to consider the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the bullet can be calculated using the formula:
Work = Change in Kinetic Energy
The initial kinetic energy of the bullet is zero since it was at rest before being fired. The final kinetic energy is given by the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Substituting the values of the mass and velocity of the bullet, we can find the final kinetic energy.
The change in kinetic energy is given by:
Change in KE = Final KE - Initial KE
So, by substituting the initial and final values of kinetic energy, we can calculate the work done on the bullet by the exploding gunpowder.
Please provide the mass of the skater (M) to proceed with calculating the recoil velocity.