A 138 lb
 golfer is pushing their 34 lb
 golf bag up a 12 ∘
 hill. The tractive force between the golfer and the ground is 91 lb
 . Assume the golfer pushes on the bag parallel to the ground and the wheels of the golf bag roll freely. what is the acceleration 

To calculate the acceleration of the golf bag, we need to analyze the forces acting on it. Here's a step-by-step breakdown:

### Step 1: Break down the forces

- **Weight of the golf bag (W_bag)**: The weight of the golf bag is given as 34 lb. We will convert this to mass using the fact that 1 lb = 1 slug · ft/s². The mass of the golf bag is:

\[
m_{\text{bag}} = \frac{34 \, \text{lb}}{32.2 \, \text{ft/s}^2} = 1.056 \, \text{slugs}
\]

- **Force due to gravity (F_gravity)**: The force of gravity on the golf bag has two components on the hill:
    - A component parallel to the hill pulling the bag down, \( F_{\text{gravity}, \parallel} \),
    - A component perpendicular to the hill, \( F_{\text{gravity}, \perp} \).

  The parallel component is given by:

\[
F_{\text{gravity}, \parallel} = W_{\text{bag}} \cdot \sin(\theta) = 34 \cdot \sin(12^\circ) \approx 34 \cdot 0.2079 \approx 7.0686 \, \text{lb}
\]

- **Tractive force (F_push)**: The golfer is applying a force parallel to the ground, so we only consider the horizontal component of the 91 lb tractive force. The effective force pushing the bag up the incline is:

\[
F_{\text{push}} = 91 \, \text{lb}
\]

### Step 2: Net force acting on the golf bag

The net force \( F_{\text{net}} \) on the bag is the difference between the pushing force and the force pulling the bag down the hill (the parallel component of gravity):

\[
F_{\text{net}} = F_{\text{push}} - F_{\text{gravity}, \parallel} = 91 - 7.0686 = 83.9314 \, \text{lb}
\]

### Step 3: Calculate the acceleration

Using Newton's second law, \( F = ma \), the acceleration \( a \) is given by:

\[
a = \frac{F_{\text{net}}}{m_{\text{bag}}} = \frac{83.9314 \, \text{lb}}{1.056 \, \text{slugs}} \approx 79.49 \, \text{ft/s}^2
\]

### Conclusion:

The acceleration of the golf bag is approximately \( 79.49 \, \text{ft/s}^2 \).

---

Do you have any questions or want further details? Here are some related questions you might consider:

1. How would the acceleration change if the incline increased to 20 degrees?
2. What would happen to the acceleration if the wheels of the golf bag didn't roll freely (added friction)?
3. How is the acceleration affected if the golfer pushes with less force (say 70 lb)?
4. What if the golf bag was heavier, say 50 lb, instead of 34 lb?
5. How do we incorporate the golfer's own weight into the problem if necessary?

**Tip:** Always double-check units, especially when switching between pounds (force) and slugs (mass).

A 138 lb golfer is pushing their 34 lb golf bag up a 12° hill. The tractive force between the golfer and the ground is 91 lb. Assume the golfer pushes on the bag parallel to the ground and the wheels of the golf bag roll freely. What is the acceleration?

Learn how to calculate the acceleration of a 34 lb golf bag pushed up a 12° incline by a 138 lb golfer with a tractive force of 91 lb. This problem involves applying Newton's Second Law, decomposing forces using trigonometry, and converting units. Suitable for Grades 10-12.

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