A 16 kg steel drum is being pushed upwards on a steel ramp that has an angle of 30 degrees with respect to the horizontal) with a force of 249 N. If the steel drum was pushed 1 meters up the ramp, what is the work done by the pushing force?.

For steel on steel the friction coefficients are μs=0.74 and μk=0.57.

To find the work done by the pushing force on the steel drum as it is moved up the ramp, we can use the formula for work:

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

where:
- \( W \) is the work done by the force,
- \( F \) is the applied force (249 N),
- \( d \) is the displacement along the direction of the force (1 m),
- \( \theta \) is the angle between the direction of the force and the direction of displacement, which in this case is 0 degrees because the force is pushing directly along the direction of displacement up the ramp.

Since the force is applied directly along the displacement, the angle \(\theta = 0^\circ\), and \(\cos 0^\circ = 1\). Thus, the work done by the force simplifies to:

\[
W = F \cdot d
\]

### Calculating Work Done by the Pushing Force

1. **Substitute the values:**
   \[
   W = 249 \, \text{N} \cdot 1 \, \text{m} = 249 \, \text{J}
   \]

Therefore, the work done by the pushing force is **249 J**.

### Additional Consideration: Friction

Since you provided coefficients of friction, we might consider whether friction plays a role in calculating the *total* work required to push the drum up the ramp. However, for this specific question, the work asked is solely due to the applied pushing force, not including work done against friction.

Would you like to see calculations that account for frictional work?

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Here are some related questions to deepen understanding:

1. What is the total work done when accounting for frictional forces?
2. How would the work change if the ramp angle was different?
3. How is the normal force on the ramp calculated for this scenario?
4. How would the frictional force impact the net force on the drum?
5. What are the implications if the drum was pushed with a force greater than 249 N?

**Tip:** Always consider if frictional forces are present, as they add an additional component to the total work required.

A 16 kg steel drum is being pushed upwards on a steel ramp that has an angle of 30 degrees with respect to the horizontal with a force of 249 N. If the steel drum was pushed 1 meter up the ramp, what is the work done by the pushing force? For steel on steel, the friction coefficients are μs=0.74 and μk=0.57.

Understand how to calculate the work done by a force pushing a 16 kg steel drum up a 30-degree inclined plane with a force of 249 N. This example covers key physics concepts, including the work-energy theorem, forces on inclined planes, and the role of friction. Suitable for students in Grades 11-12.

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