A rubber-wheeled 50 kg cart rolls down a 15 ∘ concrete incline. Coefficient of rolling friction between rubber and concrete is μr = 0.02. What is the cart's acceleration if rolling friction is neglected?

To find the cart's acceleration when rolling friction is neglected, we will only consider the forces acting on the cart due to gravity along the incline.

### Step-by-step solution:

1. **Identify forces:**
   - The gravitational force acting on the cart is \( F_g = m \cdot g \), where:
     - \( m = 50 \, \text{kg} \) is the mass of the cart,
     - \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity.

2. **Component of gravitational force along the incline:**
   The force acting along the incline is the component of the gravitational force parallel to the surface:
   \[
   F_{\text{parallel}} = F_g \cdot \sin(\theta)
   \]
   where \( \theta = 15^\circ \) is the angle of the incline.

   Therefore:
   \[
   F_{\text{parallel}} = m \cdot g \cdot \sin(15^\circ)
   \]

3. **Newton's second law:**
   Since the only force acting on the cart along the incline is \( F_{\text{parallel}} \), the net force \( F_{\text{net}} \) is equal to \( F_{\text{parallel}} \).

   Using Newton’s second law, \( F_{\text{net}} = m \cdot a \), where \( a \) is the acceleration of the cart. Thus:
   \[
   m \cdot a = m \cdot g \cdot \sin(15^\circ)
   \]
   Simplifying by canceling the mass \( m \) from both sides:
   \[
   a = g \cdot \sin(15^\circ)
   \]

4. **Calculate the acceleration:**
   \[
   a = 9.81 \, \text{m/s}^2 \cdot \sin(15^\circ)
   \]
   Using \( \sin(15^\circ) \approx 0.2588 \), we get:
   \[
   a \approx 9.81 \, \text{m/s}^2 \cdot 0.2588
   \]
   \[
   a \approx 2.54 \, \text{m/s}^2
   \]

### Final answer:
The acceleration of the cart, neglecting rolling friction, is approximately \( 2.54 \, \text{m/s}^2 \).

Would you like more details on how rolling friction would affect the result or how to include it? Here are some related questions to explore:

1. How does rolling friction impact acceleration?
2. How can we calculate acceleration including rolling friction?
3. What forces contribute to the motion of a cart on an inclined plane?
4. How is the normal force calculated for an inclined plane?
5. What is the difference between sliding friction and rolling friction?

**Tip:** When dealing with inclined planes, always break down forces into components parallel and perpendicular to the surface to simplify your calculations.

Find out how to calculate the acceleration of a 50 kg cart rolling down a 15° incline without considering rolling friction. This physics problem involves kinematics, forces, and motion, applying Newton's Second Law and gravitational forces. Perfect for high school students studying Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation