Two blocks, M = 12.0O kg and m = 5.54 kg, are connected via a massless rope. They are being pushed up a frictionless hill, with a slope of 15.5°, with a constant force in the direction of the incline, such that there is a total acceleration of 2.48 m/s² for the system. M What is the tension in the rope? Number N What is the magnitude of the force on block M? Number N

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Motion of Connected Blocks on an Inclined Plane**

**Introduction:**

In this example, we have a system consisting of two blocks connected by a massless rope. The blocks are being pushed up a frictionless incline with a constant force.

**Parameters:**

- Block M has a mass of 12.0 kg.
- Block m has a mass of 5.54 kg.
- The incline makes an angle of 15.5° with the horizontal.
- The total acceleration of the system is 2.48 m/s².

**Diagram Explanation:**

The image shows two blocks (m and M) positioned on an inclined plane. The incline is drawn with a notable angle (θ) of 15.5° with respect to the horizontal. There is an applied force pushing block M upward along the plane. Block m is positioned below block M and both are connected by a rope.

**Problem Questions:**

1. **What is the tension in the rope?**

   The objective is to find the tension within the connecting rope as the blocks accelerate up the incline.

2. **What is the magnitude of the force on block M?**

   Here, the aim is to determine the amount of force being applied to block M that causes the system to accelerate at the given rate.

This scenario can be used to explore concepts such as Newton's second law, inclined plane dynamics, and tension in connecting ropes.
Transcribed Image Text:**Title: Motion of Connected Blocks on an Inclined Plane** **Introduction:** In this example, we have a system consisting of two blocks connected by a massless rope. The blocks are being pushed up a frictionless incline with a constant force. **Parameters:** - Block M has a mass of 12.0 kg. - Block m has a mass of 5.54 kg. - The incline makes an angle of 15.5° with the horizontal. - The total acceleration of the system is 2.48 m/s². **Diagram Explanation:** The image shows two blocks (m and M) positioned on an inclined plane. The incline is drawn with a notable angle (θ) of 15.5° with respect to the horizontal. There is an applied force pushing block M upward along the plane. Block m is positioned below block M and both are connected by a rope. **Problem Questions:** 1. **What is the tension in the rope?** The objective is to find the tension within the connecting rope as the blocks accelerate up the incline. 2. **What is the magnitude of the force on block M?** Here, the aim is to determine the amount of force being applied to block M that causes the system to accelerate at the given rate. This scenario can be used to explore concepts such as Newton's second law, inclined plane dynamics, and tension in connecting ropes.
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