Physics momentum question

In summary: So just to make sure I understand, the negative velocity just means that she is moving in the opposite direction of the positive velocity, in this case, towards the space shuttle while the kit is moving away from the space shuttle. So even though the astronaut and the kit are moving in different directions, they still have opposite velocities and therefore momentum is conserved.In summary, the astronaut's safety line and thruster pack are sabotaged while she is on a space walk in a made-for-TV murder mystery. She is 200 meters from the shuttle and moving with it, but has only 4 minutes of air remaining. To get back to the shuttle, she throws her 10-kg tool kit with a speed of 8 m/s in the
  • #1

Homework Statement


You have been hired to check the technical correctness of an upcoming made-for-TV murder mystery. The mystery takes place in a space shuttle. In one scene, the astronaut's safety line is sabotaged while she is on a space walk, so she is no longer connected to the space shuttle. She checks and finds that her thruster pack has also been damaged and no longer works. She is 200 meters from the shuttle and moving with it. The is, she is not moving with respect to the shuttle. There she is drifting in space with only 4 minutes of air remaining. To get back to the shuttle, she decides to unstrap her 10-kg tool kit and throw it away with all her strength, so that it has a speed of 8 m/s. In the script, she survives, but is this correct? Her mass, including the space suit, is 80 kg. (Yes she does survive)

Homework Equations


p = mv
v = d/t
p = p'

The Attempt at a Solution


My attempt:

p = p', initial momentum 0 with respect to space shuttle
0 = m2Vfinal + (mkit)(Vkit)
0 = (70)Vfinal + (10)(8)
Vfinal = -1.14 m/s

V = 1.14 m/s
d = 200m

t = d/t
= 175 s

Time she has = 4 min
= 240 s

Therefore, she does survive.

I'm pretty sure I did it wrong though. Because the negative velocity doesn't make sense. Both the kit and her move in the same direction. Any1 wana help?
 
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  • #2
Negative velocities are acceptable. Remember, a velocity is a vector so it can be positive or negative. In this case, it just means your moving in the opposite direction (assuming you picked the toolbelt to travel in the positive direction). Of course if you're adding 2 numbers together to get 0 and the mass is always positive, one definitely needs to be negative. The problem looks correct.

Also, the kit and her do NOT move in the same direction. If that were the case, momentum would not be conserved.
 
  • #3
Pengwuino said:
Negative velocities are acceptable. Remember, a velocity is a vector so it can be positive or negative. In this case, it just means your moving in the opposite direction (assuming you picked the toolbelt to travel in the positive direction). Of course if you're adding 2 numbers together to get 0 and the mass is always positive, one definitely needs to be negative. The problem looks correct.

Also, the kit and her do NOT move in the same direction. If that were the case, momentum would not be conserved.

But say everything is stationary, then she throws the kit, doesn't that cause her to move in the same direction as the throwing movement pulls her forward? I can't really visualize this.
Also, can you expand on why those 2 things moving in same direction would not result in the conservation of momentum? I really need to understand this topic. This is going to be an easy problem compared to the questions our grade 12 teacher puts on the test.
 
  • #4
ppl k1ll3r said:
But say everything is stationary, then she throws the kit, doesn't that cause her to move in the same direction as the throwing movement pulls her forward? I can't really visualize this.
Also, can you expand on why those 2 things moving in same direction would not result in the conservation of momentum? I really need to understand this topic. This is going to be an easy problem compared to the questions our grade 12 teacher puts on the test.

Ok so everything is stationary, that is the total momentum is 0. Setup your coordinate system with the astronaut at the origin on the x-axis and the direction they want to throw it, let's say the left, along the negative x-axis. When she throws the kit to the left, the kit has momentum p = mv. v here is -8m/s because its going in the negative x-direction. Her momentum would be p = mv = (-8m/s) * (10kg). Now for momentum to be conserved, the total momentum after her throwing it has to equal 0 since that was the momentum before she threw it. In order to make up for this -80 kg*m/s momentum, she needs to have a positive 80 kg*m/s momentum so that they sum to 0 thus conserving momentum. Since her mass is always positive and in this case, 80kg, the velocity must be positive as well.

The way you setup your program is that the direction away from her was positive and the direction towards the shuttle was negative. In my example, the directions were switched (ie she went a positive velocity and the kit went with a negative velocity) but the idea is the same.
 
  • #5
Thanks, makes sense now.
 

What is momentum?

Momentum is a measurement of an object's motion, taking into account its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

What is the formula for calculating momentum?

The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

How is momentum conserved?

Momentum is conserved in a closed system, meaning that the total momentum of all objects in the system before and after a collision or interaction remains the same. This is known as the law of conservation of momentum.

What is the difference between linear and angular momentum?

Linear momentum refers to an object's motion in a straight line, while angular momentum refers to an object's rotational motion. Both are calculated using the same formula, but angular momentum also takes into account the object's moment of inertia and angular velocity.

How does momentum affect collisions?

In a collision between two objects, the total momentum before and after the collision must be equal. This means that if one object gains momentum, the other must lose an equal amount. This is known as the law of conservation of momentum and is an important concept in understanding the dynamics of collisions.

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