Questions 5, 6, and 7 refer to a block with mass m that is attached by a string with negligible mass to a solid cylinder of mass M and radius R, and is about to slide down a ramp with angle 0, as shown in the figure to the right. The coefficient of kinetic friction between the block and the ramp is, and the drum is free to rotate with no friction. Solid cylinder with mass M and radius R m 0 Coefficient of kinetic friction k 5. In the space below, draw clearly labelled free-body diagrams for the block and for the drum. 6. In conjunction with an equation for I and an equation that relates a and a, use your free-body diagrams with F = mā and Σ7 = Iā to come up with a system of equations that you could M, R, g, use to solve for the linear acceleration of the block a in terms of the variables m, Hk) and 0. But you do not need to solve this system of equations.
Questions 5, 6, and 7 refer to a block with mass m that is attached by a string with negligible mass to a solid cylinder of mass M and radius R, and is about to slide down a ramp with angle 0, as shown in the figure to the right. The coefficient of kinetic friction between the block and the ramp is, and the drum is free to rotate with no friction. Solid cylinder with mass M and radius R m 0 Coefficient of kinetic friction k 5. In the space below, draw clearly labelled free-body diagrams for the block and for the drum. 6. In conjunction with an equation for I and an equation that relates a and a, use your free-body diagrams with F = mā and Σ7 = Iā to come up with a system of equations that you could M, R, g, use to solve for the linear acceleration of the block a in terms of the variables m, Hk) and 0. But you do not need to solve this system of equations.
College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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![**Title: Physics Problem: Block and Cylinder System on an Incline**
**Description:**
Questions 5, 6, and 7 refer to a block with mass \( m \) that is attached by a string with negligible mass to a solid cylinder of mass \( M \) and radius \( R \), and is about to slide down a ramp with angle \( \theta \), as shown in the figure. The coefficient of kinetic friction between the block and the ramp is \( \mu_k \), and the drum is free to rotate with no friction.
**Diagram:**
- A solid cylinder with mass \( M \) and radius \( R \) is positioned at the top of the ramp.
- The block of mass \( m \) is situated on the inclined plane with angle \( \theta \).
- The block is connected to the cylinder by a string.
- The figure indicates the presence of kinetic friction between the block and the ramp, represented by the coefficient \( \mu_k \).
**Problems:**
5. **Free-Body Diagrams:**
Draw clearly labeled free-body diagrams for the block and for the drum.
6. **Equations and Problem-Solving:**
In conjunction with an equation for \( I \) (moment of inertia) and an equation that relates \( a \) (linear acceleration) and \( \alpha \) (angular acceleration), use your free-body diagrams with
\[
\sum \mathbf{F} = m \mathbf{a} \quad \text{and} \quad \sum \mathbf{\tau} = I \alpha
\]
to come up with a system of equations that you could use to solve for the linear acceleration of the block \( a \) in terms of the variables \( m, M, R, g, \mu_k, \) and \( \theta \). Note that you do not need to solve this system of equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03ee7fb4-b1d7-4f35-a15b-4bc6954070e5%2Fc0876a12-ac5f-47f3-bdbc-f28fa4c28987%2F8t2y616_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Physics Problem: Block and Cylinder System on an Incline**
**Description:**
Questions 5, 6, and 7 refer to a block with mass \( m \) that is attached by a string with negligible mass to a solid cylinder of mass \( M \) and radius \( R \), and is about to slide down a ramp with angle \( \theta \), as shown in the figure. The coefficient of kinetic friction between the block and the ramp is \( \mu_k \), and the drum is free to rotate with no friction.
**Diagram:**
- A solid cylinder with mass \( M \) and radius \( R \) is positioned at the top of the ramp.
- The block of mass \( m \) is situated on the inclined plane with angle \( \theta \).
- The block is connected to the cylinder by a string.
- The figure indicates the presence of kinetic friction between the block and the ramp, represented by the coefficient \( \mu_k \).
**Problems:**
5. **Free-Body Diagrams:**
Draw clearly labeled free-body diagrams for the block and for the drum.
6. **Equations and Problem-Solving:**
In conjunction with an equation for \( I \) (moment of inertia) and an equation that relates \( a \) (linear acceleration) and \( \alpha \) (angular acceleration), use your free-body diagrams with
\[
\sum \mathbf{F} = m \mathbf{a} \quad \text{and} \quad \sum \mathbf{\tau} = I \alpha
\]
to come up with a system of equations that you could use to solve for the linear acceleration of the block \( a \) in terms of the variables \( m, M, R, g, \mu_k, \) and \( \theta \). Note that you do not need to solve this system of equations.
Transcribed Image Text:**7.**
Assuming the block is starting its motion from rest, use an energy approach to find an expression for its speed (in terms of the variables given) after it has slid a distance \( d \) down the ramp.
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