A 162 lb
 golfer is pushing their 21 lb
 golf bag up a 17 ∘
 hill. The tractive force between the golfer and the ground is 96 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'll break down the forces acting on it and apply Newton's second law of motion.

### Given Data:
- Weight of the golfer: \( W_g = 162 \, \text{lb} \)
- Weight of the golf bag: \( W_b = 21 \, \text{lb} \)
- Tractive force between golfer and ground: \( F_t = 96 \, \text{lb} \)
- Incline angle: \( \theta = 17^\circ \)

### Assumptions:
1. The golfer is pushing the bag parallel to the ground.
2. The wheels of the bag are rolling freely, so there is no friction between the bag and the surface.
3. The tractive force acts entirely to push the bag.

### Step 1: Resolve Forces

The tractive force is used to push the golf bag up the incline. The weight of the bag has two components:
- **Parallel to the incline (opposing motion)**: This component will oppose the tractive force, \( W_b \sin(\theta) \).
- **Perpendicular to the incline**: This component doesn’t affect the acceleration of the bag, \( W_b \cos(\theta) \).

### Step 2: Newton's Second Law

To determine the acceleration, we can apply Newton's second law along the direction of the incline. The net force along the incline direction is the tractive force minus the component of the golf bag's weight parallel to the incline:

\[
F_{\text{net}} = F_t - W_b \sin(\theta)
\]

This net force will accelerate the golf bag. Using Newton's second law:

\[
F_{\text{net}} = m_b a
\]

where:
- \( m_b \) is the mass of the bag,
- \( a \) is the acceleration of the bag.

We need to convert the weight of the bag into mass using the relation:

\[
m_b = \frac{W_b}{g}
\]

where \( g \approx 32.2 \, \text{ft/s}^2 \) is the acceleration due to gravity.

### Step 3: Calculate Mass and Force

Let's now calculate these values step by step.The acceleration of the golf bag is approximately \( 137.79 \, \text{ft/s}^2 \).

This value seems quite large, which may indicate an idealized situation where friction is completely neglected and the tractive force is very strong relative to the bag's weight.

Would you like more details on any part of the process, or have additional questions?

Here are 5 related questions:
1. How would friction between the golf bag and the surface change the result?
2. What if the incline of the hill was steeper? How would that affect acceleration?
3. How would the result change if the golfer's pushing force wasn't perfectly parallel to the ground?
4. How can we calculate the work done by the golfer in pushing the bag up the hill?
5. How would the acceleration change if the mass of the golf bag were doubled?

**Tip**: When dealing with inclined planes, always break forces into components parallel and perpendicular to the incline for better accuracy in calculations.

A 162 lb golfer is pushing their 21 lb golf bag up a 17 ∘ hill. The tractive force between the golfer and the ground is 96 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 21 lb golf bag pushed by a 162 lb golfer up a 17-degree hill using Newton's Second Law and trigonometry. The solution involves resolving forces on inclined planes and calculating acceleration. Ideal for high school students studying physics.

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