A rocket ship at rest in space gives a short blast of its engine, firing 26 kg of exhaust gas out the back end with an average velocity of 182 m/s. What is the change in momentum of the rocket during this blast?
Δp(rocket)=Δp(gas)= mv=26•182=4732 kg•m/s
To find the change in momentum of the rocket, we need to calculate the momentum of the exhaust gas and then subtract it from the initial momentum of the rocket.
The momentum of an object is given by the equation: momentum = mass * velocity.
Given:
Mass of the exhaust gas (m) = 26 kg
Velocity of the exhaust gas (v) = 182 m/s
First, let's calculate the momentum of the exhaust gas:
Momentum of the exhaust gas = mass * velocity
= 26 kg * 182 m/s
= 4732 kg m/s
Since the rocket is initially at rest, its momentum is zero.
Initial momentum of the rocket = 0 kg m/s
Now, let's calculate the change in momentum of the rocket by subtracting the momentum of the exhaust gas from its initial momentum:
Change in momentum of the rocket = Final momentum - Initial momentum
= -4732 kg m/s (Note that the negative sign indicates the opposite direction of momentum)
Therefore, the change in momentum of the rocket during this blast is -4732 kg m/s.