A 135 lb golfer is pushing their 23 lb golf bag up a 20 ∘ hill. The tractive force between the golfer and the ground is 92 lb. Assume the golfer pushes on the bag parallel to the ground and the wheels of the golf bag roll freely. Determine the acceleration of the golf bag. 

To determine the acceleration of the golf bag, we need to analyze the forces acting on the bag and then apply Newton's second law of motion.

### Step 1: Break down forces acting on the golf bag

- **Weight of the bag**: The weight \( W_{\text{bag}} \) is given by
  \[
  W_{\text{bag}} = 23 \text{ lb}.
  \]

- **Component of the bag's weight parallel to the incline**: Since the hill is at an angle of \( 20^\circ \), the component of the bag’s weight parallel to the incline is:
  \[
  W_{\parallel} = W_{\text{bag}} \cdot \sin(20^\circ).
  \]

- **Component of the bag's weight perpendicular to the incline**: The component of the weight perpendicular to the incline doesn't contribute to the motion along the incline, but it affects normal force and friction (though friction is ignored since the wheels roll freely). This is:
  \[
  W_{\perp} = W_{\text{bag}} \cdot \cos(20^\circ).
  \]

- **Force applied by the golfer**: The golfer is applying a tractive force parallel to the ground \( F_{\text{tract}} = 92 \text{ lb} \). This force needs to be broken into components parallel and perpendicular to the incline.

  The component of the golfer's applied force parallel to the incline is:
  \[
  F_{\parallel} = F_{\text{tract}} \cdot \cos(20^\circ).
  \]

  The component of the golfer's applied force perpendicular to the incline is:
  \[
  F_{\perp} = F_{\text{tract}} \cdot \sin(20^\circ).
  \]

### Step 2: Apply Newton's Second Law

The net force acting on the golf bag along the incline is:
\[
F_{\text{net}} = F_{\parallel} - W_{\parallel}.
\]
This net force causes the acceleration of the golf bag. Using Newton's second law \( F = ma \), where \( m \) is the mass of the golf bag and \( a \) is its acceleration, we get:
\[
F_{\text{net}} = m a.
\]
To find the mass \( m \), we convert the weight of the golf bag from pounds to slugs. Since \( 1 \text{ slug} = 32.2 \text{ lb} \), the mass of the golf bag is:
\[
m = \frac{W_{\text{bag}}}{32.2}.
\]

Finally, solve for the acceleration:
\[
a = \frac{F_{\text{net}}}{m}.
\]

### Step 3: Calculation

Now we can plug in the numbers and calculate the acceleration.

1. \( W_{\parallel} = 23 \cdot \sin(20^\circ) \)
2. \( F_{\parallel} = 92 \cdot \cos(20^\circ) \)
3. \( m = \frac{23}{32.2} \)
4. \( F_{\text{net}} = F_{\parallel} - W_{\parallel} \)
5. \( a = \frac{F_{\text{net}}}{m} \)

Let me calculate the value of \( a \).The acceleration of the golf bag is approximately \( 110.02 \, \text{ft/s}^2 \).

Would you like further details or have any questions?

Here are five related questions you might find useful:
1. What effect does increasing the incline angle have on the acceleration?
2. How would the acceleration change if the golfer applied a larger tractive force?
3. How would friction affect the acceleration if the wheels didn't roll freely?
4. What is the difference between weight and mass in these types of problems?
5. How would the result differ if the bag were being pulled up instead of pushed?

**Tip:** Always break forces into components parallel and perpendicular to the incline when solving incline problems!

A 135 lb golfer is pushing their 23 lb golf bag up a 20° hill. The tractive force between the golfer and the ground is 92 lb. Assume the golfer pushes on the bag parallel to the ground and the wheels of the golf bag roll freely. Determine the acceleration of the golf bag.

Determine the acceleration of a 23 lb golf bag pushed by a 135 lb golfer up a 20° hill. Learn how to break down forces using Newton's Second Law of Motion and trigonometry, with step-by-step calculations of weight components, tractive force, and acceleration. Suitable for high school physics students in Grades 10-12.

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