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
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
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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,
the angle of inclination of the rough plane,
coefficient of friction between package A and the plane is,
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