An astronaut whose mass is 80. kg carries an empty oxygen tank with a mass of 10. kg. The astronaut throws the tank away with a speed of 2.0 m/s. With what velocity does the astronaut start to move off into space?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
Let's consider the astronaut and the oxygen tank as our system. Before the astronaut throws the tank, both the astronaut and the tank are at rest, so their initial momentum is zero.
Let's denote the velocity of the astronaut after throwing the tank as V_a, and the velocity of the tank after being thrown as V_t. The mass of the astronaut is 80. kg, and the mass of the tank is 10. kg.
According to the conservation of momentum, we can write the equation:
(mass of astronaut * velocity of astronaut) + (mass of tank * velocity of tank) = 0
(80. kg * V_a) + (10. kg * 2.0 m/s) = 0
80. kg * V_a = - (10. kg * 2.0 m/s)
80. kg * V_a = - 20. kg * m/s
Now we can solve for V_a by isolating it on one side of the equation:
V_a = - (20. kg * m/s) / 80. kg
V_a = - 0.25 m/s
Therefore, the astronaut starts to move off into space with a velocity of -0.25 m/s. The negative sign indicates that the astronaut is moving in the opposite direction of the thrown tank.
To find the velocity with which the astronaut starts to move off into space, we can use the principle of conservation of momentum. The total momentum before throwing the tank away is equal to the total momentum after throwing it away.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m × v
Before throwing the tank away, the total momentum is the sum of the momentum of the astronaut and the momentum of the tank. After throwing it away, the momentum is only from the astronaut:
Total momentum before = Total momentum after
(mass of astronaut × velocity of astronaut) + (mass of tank × velocity of tank) = mass of astronaut × velocity of astronaut in space
Substituting the given values:
(80. kg × velocity of astronaut) + (10. kg × 2.0 m/s) = 80. kg × ??? m/s
Now, we can solve this equation to find the velocity of the astronaut. Rearranging the equation:
80. kg × velocity of astronaut = (10. kg × 2.0 m/s)
Dividing both sides of the equation by 80. kg:
velocity of astronaut = (10. kg × 2.0 m/s) / 80. kg
Calculating this, we find:
velocity of astronaut = 0.5 m/s
Therefore, the astronaut starts to move off into space with a velocity of 0.5 m/s.
momentum is conserved.
80*V+10(-2)=0
solve for V