Conservation of momentum of astronaut in her space suit

[mandy9008]

Homework Statement

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.

Homework Equations

m1v1i + m2v2i = m1v1f + m2v2f

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.

 

[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.

 

[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

 

[inky]

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

I think you need to consider projectile motion concept.

 

[ehild]

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

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

 

[mandy9008]

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

 

[ehild]

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

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

ehild

 

[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

 

[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

 

[kuruman]

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

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.

 

[mandy9008]

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

 

[Doc Al]

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

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.

 

[mandy9008]

okay that makes sense. x=123.5 m Thank You