17. Two packages are connected by a very light string that goes over an ideal pulley as shown in the figure. Package A has a mass of 3.0 kg and can slide along a rough plane inclined at 30° above the horizontal. The string acts on package A parallel to the surface of the plane. The coefficient of static friction between package A and the plane is 0.40. What minimum mass should package B have in order to start package A sliding up the ramp? 30° A B

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**Title: Understanding Static Friction and Inclined Planes**

**Educational Content:**

**Problem Statement:**

Two packages are connected by a very light string that goes over an ideal pulley, as illustrated in the diagram. Package A has a mass of 3.0 kg and can slide along a rough plane inclined at 30° above the horizontal. The string exerts a force parallel to the surface of the plane. The coefficient of static friction between Package A and the plane is 0.40. What minimum mass should Package B have in order to start Package A sliding up the ramp?

**Diagram Explanation:**

The diagram shows:

1. An inclined plane with an angle of 30°.
2. Package A, with a labeled mass of 3.0 kg, placed on the inclined plane.
3. Package B is hanging vertically, connected to Package A via a string passing over a pulley.
4. The pulley is assumed to be ideal (frictionless and massless).

In the problem:

- The inclined plane provides resistance through static friction.
- The goal is to determine Package B's mass needed to overcome static friction and move Package A upward.

**Key Concepts:**

- **Static Friction:** A force that resists the initial motion of an object. It acts opposite to the direction of the intended movement and must be overcome to initiate sliding.
- **Net Force Calculation:** To find the mass of Package B, calculate the forces acting on Package A (gravity, normal force, and static friction) and solve for the force needed to overcome these.
- **Inclined Plane Mechanics:** Analyze the components of forces parallel and perpendicular to the plane to solve for the unknown mass.
Transcribed Image Text:**Title: Understanding Static Friction and Inclined Planes** **Educational Content:** **Problem Statement:** Two packages are connected by a very light string that goes over an ideal pulley, as illustrated in the diagram. Package A has a mass of 3.0 kg and can slide along a rough plane inclined at 30° above the horizontal. The string exerts a force parallel to the surface of the plane. The coefficient of static friction between Package A and the plane is 0.40. What minimum mass should Package B have in order to start Package A sliding up the ramp? **Diagram Explanation:** The diagram shows: 1. An inclined plane with an angle of 30°. 2. Package A, with a labeled mass of 3.0 kg, placed on the inclined plane. 3. Package B is hanging vertically, connected to Package A via a string passing over a pulley. 4. The pulley is assumed to be ideal (frictionless and massless). In the problem: - The inclined plane provides resistance through static friction. - The goal is to determine Package B's mass needed to overcome static friction and move Package A upward. **Key Concepts:** - **Static Friction:** A force that resists the initial motion of an object. It acts opposite to the direction of the intended movement and must be overcome to initiate sliding. - **Net Force Calculation:** To find the mass of Package B, calculate the forces acting on Package A (gravity, normal force, and static friction) and solve for the force needed to overcome these. - **Inclined Plane Mechanics:** Analyze the components of forces parallel and perpendicular to the plane to solve for the unknown mass.
Expert Solution
Step 1

mass of package, mA=3 Kg

the angle of inclination of the rough plane, θ=30°

coefficient of friction between package A and the plane is,μs=0.4

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