# Homework Help: Conservation of momentum of astronaut in her space suit

1. Jun 27, 2010

### mandy9008

1. The problem statement, all variables and given/known data
An astronaut in her space suit has a total mass of m1 = 91.3 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft, she throws her oxygen tank of mass m2 = 12.0-kg away from her spacecraft with a speed v = 8.50 m/s to propel herself back toward it (see figure).

(a) Determine the maximum distance she can be from the craft and still return within 1.60 min (the amount of time the air in her helmet remains breathable).
(b) Explain in terms of Newton's laws of motion why this strategy works.

2. Relevant equations
m1v1i + m2v2i = m1v1f + m2v2f

3. The attempt at a solution
a. (91.3 kg)(0 m/s) + (12.0 kg)(0 m/s) = (91.3 kg)v1f + (12.0 kg)(8.50 m/s)
v1f=1.112 m/s
b. When the astronaut throws her oxygen tank, she applies a force onto it. At the same time, the oxygen tank is applying a force onto her, which pushes the astronaut towards the space ship. This is an example of Newton's Third Law.

2. Jun 27, 2010

### kuruman

You calculate the speed correctly in part (a), but that's not what the problem is asking for. You need to find a maximum distance.

Part (b) is OK.

3. Jun 27, 2010

### mandy9008

okay, so I need to solve for change in x, right?
x=vt + 1/2 gt^2
x= (1.118 m/s)(96 s) + 1/2 (9.8 m/s^2)(96s)^2
x=45265.7 m

that does not seem right at all

4. Jun 27, 2010

### inky

I think you need to consider projectile motion concept.

5. Jun 27, 2010

### ehild

The astronaut is in free space, not on the surface of Earth!! Is there any force acting on she after she has thrown the oxygen tank away? This is not a projectile motion.

ehild

6. Jun 27, 2010

### mandy9008

okay so, do i need to find her acceleration and use that in place of g?

7. Jun 27, 2010

### ehild

You know that acceleration is force over mass. What can exert force on the astronaut in free space?

ehild

8. Jun 27, 2010

### mandy9008

I don't know. I know that it is not gravitational, since you said that I can't use 9.8 m/s^2

9. Jun 28, 2010

### ehild

Is gravitational acceleration 9.8 m/s^2 everywhere in the world? On the surface of the Moon for example? Have you seen films about astronauts walking on the Moon?

There is gravitational interaction between any objects with mass. Do you know the formula?

ehild

10. Jun 28, 2010

### kuruman

Repeat the calculation using the same equation with zero acceleration and you are done. Although there is gravitational attraction between the spacecraft and the astronaut, it should be considered negligible. Besides, the mass of the spacecraft is not given so you cannot calculate it.

11. Jun 28, 2010

### mandy9008

x= (1.118 m/s)(96 s) + 1/2 (0 m/s^2)(96 s)^2
x=107.328m
this is not correct.

12. Jun 28, 2010

### Staff: Mentor

You made an error here. 91.3 kg is her total mass including suit and oxygen tank. If her oxygen tank is 12 kg, what's the mass of her and her suit?

Redo this to get the correct speed after she throws the tank.

13. Jun 28, 2010

### mandy9008

okay that makes sense. x=123.5 m Thank You

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