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A cable is attached to a 1.40 kg block A, is looped over a fixed peg at C, and is attached to plate B.(Figure 1) The coefficient of static friction between the plate and the block is HA = 0.150, the coefficient of static friction between the plate and the inclined plane is µB = 0.300, and the coefficient of static friction between the cable and the peg is µc = 7.00×10-2. If the plane's angle is 30.0 degrees, what is the maximum mass that plate B can have such that it does not slide down the plane? Express your answer numerically in kilograms to three significant figures. • View Available Hint(s) vec mB = kg

A cable is attached to a 1.40 kg block A, is looped over a fixed peg at C, and is attached to plate B.(Figure 1) The coefficient of static friction between the plate and the block is HA = 0.150, the coefficient of static friction between the plate and the inclined plane is µB = 0.300, and the coefficient of static friction between the cable and the peg is µc = 7.00×10-2. If the plane's angle is 30.0 degrees, what is the maximum mass that plate B can have such that it does not slide down the plane? Express your answer numerically in kilograms to three significant figures. • View Available Hint(s) vec mB = kg

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem Statement for Educational Website** --- A cable is attached to a 1.40 kg block \(A\), is looped over a fixed peg at \(C\), and is attached to plate \(B\). (Figure 1) The coefficient of static friction between the plate and the block is \(\mu_A = 0.150\), the coefficient of static friction between the plate and the inclined plane is \(\mu_B = 0.300\), and the coefficient of static friction between the cable and the peg is \(\mu_C = 7.00 \times 10^{-2}\). If the plane's angle is 30.0 degrees, what is the maximum mass that plate \(B\) can have such that it does not slide down the plane? Express your answer numerically in kilograms to three significant figures. **Answer Box:** --- mp = _________ kg
Transcribed Image Text:**Problem Statement for Educational Website** --- A cable is attached to a 1.40 kg block \(A\), is looped over a fixed peg at \(C\), and is attached to plate \(B\). (Figure 1) The coefficient of static friction between the plate and the block is \(\mu_A = 0.150\), the coefficient of static friction between the plate and the inclined plane is \(\mu_B = 0.300\), and the coefficient of static friction between the cable and the peg is \(\mu_C = 7.00 \times 10^{-2}\). If the plane's angle is 30.0 degrees, what is the maximum mass that plate \(B\) can have such that it does not slide down the plane? Express your answer numerically in kilograms to three significant figures. **Answer Box:** --- mp = _________ kg
### Inclined Plane and Friction Analysis #### Figure Description The figure illustrates a classic physics problem involving an inclined plane and friction forces. Key elements in the diagram include: 1. **Inclined Plane**: The plane is inclined at an angle \(\theta\) with respect to the horizontal ground. 2. **Block A**: This block is situated on the inclined plane and has a contact friction coefficient \(\mu_A\) with the surface of the plane. 3. **Surface B**: Represents another surface at the base which has a contact friction coefficient \(\mu_B\). 4. **Pulley C**: A rope passes over a pulley located at point C. The pulley has a coefficient of friction \(\mu_C\). #### Forces and Motion - **Gravitational Force on Block A**: Acts vertically downward. - **Normal Force from the Inclined Plane on Block A**: Perpendicular to the surface of the inclined plane. - **Frictional Force between Block A and the Inclined Plane**: Opposes the motion or potential motion of Block A parallel to the plane, characterized by \(\mu_A\). - **Frictional Force between Surface B and the Ground**: Opposes motion or potential lateral motion, characterized by \(\mu_B\). - **Tension in the Rope Over the Pulley**: Dictates the interaction between block A and any additional weights or forces applied to the other end of the rope via the pulley. This setup is often used in physics to teach principles such as Newton's laws of motion, the components of forces on inclined planes, frictional forces, and equilibrium of forces. The study of this system can involve calculating the net force on Block A, determining if Block A will slide down the plane, and analyzing the effect of different friction coefficients on the motion of the system.
Transcribed Image Text:### Inclined Plane and Friction Analysis #### Figure Description The figure illustrates a classic physics problem involving an inclined plane and friction forces. Key elements in the diagram include: 1. **Inclined Plane**: The plane is inclined at an angle \(\theta\) with respect to the horizontal ground. 2. **Block A**: This block is situated on the inclined plane and has a contact friction coefficient \(\mu_A\) with the surface of the plane. 3. **Surface B**: Represents another surface at the base which has a contact friction coefficient \(\mu_B\). 4. **Pulley C**: A rope passes over a pulley located at point C. The pulley has a coefficient of friction \(\mu_C\). #### Forces and Motion - **Gravitational Force on Block A**: Acts vertically downward. - **Normal Force from the Inclined Plane on Block A**: Perpendicular to the surface of the inclined plane. - **Frictional Force between Block A and the Inclined Plane**: Opposes the motion or potential motion of Block A parallel to the plane, characterized by \(\mu_A\). - **Frictional Force between Surface B and the Ground**: Opposes motion or potential lateral motion, characterized by \(\mu_B\). - **Tension in the Rope Over the Pulley**: Dictates the interaction between block A and any additional weights or forces applied to the other end of the rope via the pulley. This setup is often used in physics to teach principles such as Newton's laws of motion, the components of forces on inclined planes, frictional forces, and equilibrium of forces. The study of this system can involve calculating the net force on Block A, determining if Block A will slide down the plane, and analyzing the effect of different friction coefficients on the motion of the system.
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