The figure below shows an object with mass m = 5.2 kg pulled up a ramp inclined at an angle of 8 = 26° with a force of magnitude F = 32 N parallel to the ramp. (a) If there is no friction between the object and the ramp, what is the magnitude of the object's acceleration (in m/s)?

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding Inclined Planes and Forces**

**Description:**

The figure below illustrates an object with mass \(m = 5.2 \, \text{kg}\) being pulled up a ramp that is inclined at an angle of \(\theta = 26^\circ\). The pulling force \(F\) has a magnitude of \(32 \, \text{N}\) and acts parallel to the ramp.

- **Diagram Explanation:** The diagram shows a triangular ramp with an angle \(\theta\). An object with mass \(m\) is on the ramp, and a force \(\vec{F}\) is applied parallel to the surface, pointing up the incline.

**Problem Statement:**

(a) If there is no friction between the object and the ramp, what is the magnitude of the object's acceleration (in \(\text{m/s}^2\))?
   - Solution: \(1.853 \, \text{m/s}^2\)

(b) If instead the coefficient of kinetic friction between the object and the ramp is \(0.12\), what is the magnitude of the object's acceleration (in \(\text{m/s}^2\))?

**Additional Resources:**

Need Help?  
Click on "Read It" for more detailed explanations and step-by-step solutions.

**Important Note:** Understanding the effects of forces on inclined planes is crucial in physics, as it combines concepts of gravity, friction, and vector analysis, providing a strong foundation for further study in mechanics.
Transcribed Image Text:**Title: Understanding Inclined Planes and Forces** **Description:** The figure below illustrates an object with mass \(m = 5.2 \, \text{kg}\) being pulled up a ramp that is inclined at an angle of \(\theta = 26^\circ\). The pulling force \(F\) has a magnitude of \(32 \, \text{N}\) and acts parallel to the ramp. - **Diagram Explanation:** The diagram shows a triangular ramp with an angle \(\theta\). An object with mass \(m\) is on the ramp, and a force \(\vec{F}\) is applied parallel to the surface, pointing up the incline. **Problem Statement:** (a) If there is no friction between the object and the ramp, what is the magnitude of the object's acceleration (in \(\text{m/s}^2\))? - Solution: \(1.853 \, \text{m/s}^2\) (b) If instead the coefficient of kinetic friction between the object and the ramp is \(0.12\), what is the magnitude of the object's acceleration (in \(\text{m/s}^2\))? **Additional Resources:** Need Help? Click on "Read It" for more detailed explanations and step-by-step solutions. **Important Note:** Understanding the effects of forces on inclined planes is crucial in physics, as it combines concepts of gravity, friction, and vector analysis, providing a strong foundation for further study in mechanics.
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