Don is pushing a barrel up a ramp that is 1.5 meters long. He is using a force of 534 newtons acting parallel to the surface of the ramp and the ramp is at an incline of 25° from the ground. How much work is he doing to push the barrel up the entire ramp?

The work done by Don in pushing the barrel up the ramp is calculated using the following formula:

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

Where:
- \( W \) is the work done (in joules),
- \( F \) is the force applied (in newtons),
- \( d \) is the distance over which the force is applied (in meters),
- \( \theta \) is the angle between the force and the direction of motion (in degrees).

In this case:
- \( F = 534 \, \text{N} \) (force applied by Don),
- \( d = 1.5 \, \text{m} \) (length of the ramp),
- \( \theta = 0^\circ \) because the force is applied parallel to the ramp, so no angle correction is needed (cosine of 0° is 1).

Thus, the work done will simply be:
\[
W = 534 \, \text{N} \times 1.5 \, \text{m} \times \cos(0^\circ)
\]

Let’s calculate the work done.# Given values
force = 534  # N
distance = 1.5  # meters
angle = 0  # degrees because the force is parallel to the ramp

# Calculate work done
work_done = force * distance * math.cos(math.radians(angle))

# Output the work done
work_doneDon is doing **801 joules** of work to push the barrel up the entire ramp.

Do you want further clarification or have any questions?

Here are 5 related questions you might find interesting:
1. How would the work change if Don was pushing at an angle instead of parallel to the ramp?
2. How does the incline of the ramp affect the amount of work needed to push the barrel up?
3. What is the work done if the barrel is being pushed up a frictionless surface?
4. How much force would Don need if the ramp was twice as long but at the same incline?
5. What is the gravitational potential energy gained by the barrel after it reaches the top?

**Tip:** Work is maximized when the force is applied parallel to the direction of motion, as the angle between them is zero (cosine of 0° is 1).

Calculate the work done by Don pushing a barrel up a 1.5-meter ramp inclined at 25° using a force of 534 newtons. Understand the application of the work formula and its components. Suitable for high school students studying mechanics and energy calculations.

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