Conservation of momentum for a robot on a space platform

  • #1
resurgance2001
197
9
Homework Statement
While constructing a space platform, a 95.0 kg robot is standing on a 25.0 m long, 330. kg steel beam that is floating in space, initially motionless relative to the platform and pointing towards the platform which is not attached. Using its magnetic feet the robot starts walking along the beam in the direction of the platform at 1.40 m/s relative to the beam. What is the robot's velocity relative to the platform in m/s?
Relevant Equations
Conservation of momentum.
The momentum of the robot is 95.0 x 1.4 m/s towards the platform. This must be equal and opposite to the momentum imparted to the beam. Dividing 133 kg m/s by 330.0 Kg gives a velocity of 0.403 m/s for the beam. So the relative velocity of the robot relative to the platform is 1.40 - 0.403 = 0.997 m/s. But the computer says this is the wrong answer! Have I missed something? Thanks in advance for any suggestions.
 

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  • #2
Your calculation seems correct to me.
 
  • #3
resurgance2001 said:
Dividing 133 kg m/s by 330.0 Kg gives a velocity of 0.403 m/s for the beam.
That assumes 1.4 is the robot's velocity relative to the platform. It's not. It's the velocity relative to the beam.
To solve this you need to write two equations, for the two unknowns: let x and y be the velocity towards the platform of robot and beam respectively. Your first equation comes from the fact that x-y is the robot's velocity relative to the beam, which is given. Your second comes from conservation of momentum.
 
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Related to Conservation of momentum for a robot on a space platform

What is the principle of conservation of momentum?

The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act upon it. In other words, the total momentum before any event must equal the total momentum after the event, provided no external forces interfere.

How does conservation of momentum apply to a robot on a space platform?

In the context of a robot on a space platform, conservation of momentum means that any action the robot takes, such as moving or throwing an object, will result in an equal and opposite reaction by the platform. Since there are no external forces in the vacuum of space, the total momentum of the robot-platform system remains constant.

What happens if the robot moves on the space platform?

If the robot moves on the space platform, the platform will move in the opposite direction to conserve momentum. For example, if the robot walks forward, the platform will move backward to ensure that the total momentum of the system remains unchanged.

How can the robot control its movement on the space platform?

The robot can control its movement by considering the conservation of momentum. For instance, it can use internal mechanisms like reaction wheels or thrusters to change its orientation without causing significant displacement of the platform. Alternatively, it can move objects or parts of itself to generate the necessary counter-momentum.

Why is it important to consider conservation of momentum for space missions?

Conservation of momentum is crucial for space missions because it impacts the stability and control of spacecraft and robots. Understanding and applying this principle ensures that movements and operations in space are predictable and manageable, preventing unintended drifts or rotations that could jeopardize the mission's success.

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