An 1520-N crate is to be held in place on a ramp that nises at 30.0° above the horizontal. The massless rope attached to the crate makes a 22.0° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp is µs = 0.650. The pulley has no appreciable mass or friction. Draw a free-body diagrum for masses Can What is the MAXImum weight w that this crate stationary on the 7 ramp L Crate 30.0⁰ 22.0 Tamp w = ? be used to hold
An 1520-N crate is to be held in place on a ramp that nises at 30.0° above the horizontal. The massless rope attached to the crate makes a 22.0° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp is µs = 0.650. The pulley has no appreciable mass or friction. Draw a free-body diagrum for masses Can What is the MAXImum weight w that this crate stationary on the 7 ramp L Crate 30.0⁰ 22.0 Tamp w = ? be used to hold
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter6: Applications Of Newton’s Laws Of Motion
Section: Chapter Questions
Problem 24PQ: Lisa measured the coefficient of static friction between two pairs of running shoes and the track in...
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Transcribed Image Text:### Physics Problem: Analyzing Forces on an Inclined Plane
**Problem Statement:**
An object, specifically a crate with a weight of 1520 N, is positioned on an incline that rises at an angle of 30.0 degrees from the horizontal. The crate is connected via a massless rope, which extends at an angle of 22.0 degrees above the ramp's surface. The static friction coefficient (\( \mu_s \)) between the crate and the ramp is 0.650, and it is assumed that the pulley involved in the setup has neither significant mass nor friction.
**Tasks:**
1. Draw a free-body diagram illustrating all forces acting on the masses.
2. Determine the maximum weight (\( w \)) that can keep the crate stationary on the ramp.
**Diagram Explanation:**
The diagram shows a crate on an inclined plane (ramp) which is at a 30.0-degree angle with respect to the horizontal. A rope is attached to the crate and goes over a pulley, pulling a separate hanging weight labeled \( w = ? \). The rope makes a 22.0-degree angle with the surface of the incline, not aligned with the direct incline angle.
In the free-body diagram, the forces that need to be accounted for include:
- The gravitational force acting on the crate (1520 N, directed downwards).
- Frictional force opposing the motion (static friction).
- Tension in the rope acting in the direction that opposes slipping down the ramp.
- Normal force acting perpendicular to the surface of the incline.
By analyzing these forces, one can determine the conditions for equilibrium and solve for the maximum allowable weight \( w \) that maintains the crate in a stationary position on the ramp.
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