Astronauts in space move a toolbox from its initial position
m to its final position
m. The two astronauts each push on the box with a constant force. Astronaut 1 exerts a force
N and astronaut 2 exerts a force
N.
What is the total work performed on the toolbox?

To calculate the total work performed on the toolbox, we use the formula for work:

\[
W = F \cdot d \cdot \cos(\theta)
\]

Where:
- \(W\) is the work done,
- \(F\) is the total force exerted on the object,
- \(d\) is the displacement of the object,
- \(\theta\) is the angle between the force and the direction of the displacement.

Here’s what we need to know to calculate the total work:
1. The forces applied by the two astronauts.
2. The displacement (initial position and final position of the toolbox).
3. The angle at which the forces are applied relative to the direction of motion (if the forces are in the same direction as the displacement, \(\theta = 0^\circ\) and \(\cos(0^\circ) = 1\)).

If you provide the missing information:
- The magnitude of the forces (\(F_1\) and \(F_2\)),
- The displacement (\(d\)),
- The angles at which the forces are applied (or if they’re in the direction of the displacement),

I can help you calculate the total work done by the astronauts.

Do you have any further details, or would you like clarification?

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Here are 5 related questions that expand on the concept of work and force:
1. How do forces applied at an angle affect the work done on an object?
2. What happens if the forces are not constant during displacement?
3. How do you calculate work if one of the astronauts is pushing in the opposite direction?
4. What is the difference between positive work and negative work?
5. How does work-energy theorem relate to the total work done on an object?

**Tip:** When forces are applied at angles to displacement, only the component of the force in the direction of motion contributes to the work.

Astronauts in space move a toolbox from its initial position to its final position. The two astronauts each push on the box with a constant force. Astronaut 1 exerts a force of F1 N and astronaut 2 exerts a force of F2 N. What is the total work performed on the toolbox?

Learn how to calculate the total work performed on a toolbox in space when two astronauts apply constant forces. This problem covers key physics concepts, including the work formula, vector components, and the work-energy theorem. Suitable for high school students in Grades 10-12.

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