In the figure, two 6.90 kg blocks are connected by a massless string over a pulley of radius 1.90 cm and rotational inertia 7.40 × 10-4 kg·m2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.600 rad in 152 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T1, and (d) string tension T2? Assume free-fall acceleration to be equal to 9.81 m/s2. Part A is 51.94, Part B is .986, and Part C is 60.89. I just need Part D. ### Tension in a Two-Block System with a PulleyThe diagram shown depicts a mechanical setup with two blocks connected by a string that passes over a pulley. This system is often used in physics to illustrate principles of mechanics, specifically the forces of tension and gravity at play.**Components of the System:**1. **Block on the Surface (T₂):** This is the block placed on a horizontal surface. 2. **Hanging Block (T₁):** This block hangs vertically, suspended by the string passing over the pulley.3. **Pulley:** It allows the string to pass smoothly from the horizontal to the vertical direction, facilitating the motion of both blocks.**Label Explanation:**- **T₂:** The tension in the part of the string connected to the block on the surface.- **T₁:** The tension in the part of the string connected to the hanging block.**Forces in Play:**- **Weight of the Hanging Block:** Acts downward due to gravity and equals the mass of the block multiplied by gravitational acceleration (W = mg).- **Tension in the String (T₁ and T₂):** The force exerted by the string on both blocks. If the pulley is frictionless and the string is massless, the tension throughout the string remains the same.**Exploration:**To analyze this system, assume the following:- The string is inextensible and massless.- The pulley is frictionless.- The surface upon which T₂ rests is smooth to simplify calculations.### Newton’s Second Law Application1. **For the Hanging Block (T₁):** - Apply Newton's second law \(T - mg = ma\).2. **For the Block on the Surface (T₂):** - If there's no friction, \(T = ma\).### Calculation StepsTo solve for the acceleration \(a\) and tensions \(T₁\) and \(T₂\):- Identify the masses of the blocks (m₁ for the hanging block, m₂ for the block on the surface).- Set up the equations of motion.- Solve for the unknowns using algebra.By analyzing each component and the forces acting on them, students can better understand the dynamics of pulley systems and the interplay of different forces.

Answered: In the figure, two 6.90 kg blocks are…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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)...

See similar textbooks

Related questions

Question

In the figure, two 6.90 kg blocks are connected by a massless string over a pulley of radius 1.90 cm and rotational inertia 7.40 × 10^-4 kg·m². The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.600 rad in 152 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T₁, and (d) string tension T₂? Assume free-fall acceleration to be equal to 9.81 m/s².

Part A is 51.94, Part B is .986, and Part C is 60.89. I just need Part D.

### Tension in a Two-Block System with a Pulley

The diagram shown depicts a mechanical setup with two blocks connected by a string that passes over a pulley. This system is often used in physics to illustrate principles of mechanics, specifically the forces of tension and gravity at play.

**Components of the System:**
1. **Block on the Surface (T₂):** This is the block placed on a horizontal surface.
2. **Hanging Block (T₁):** This block hangs vertically, suspended by the string passing over the pulley.
3. **Pulley:** It allows the string to pass smoothly from the horizontal to the vertical direction, facilitating the motion of both blocks.

**Label Explanation:**
- **T₂:** The tension in the part of the string connected to the block on the surface.
- **T₁:** The tension in the part of the string connected to the hanging block.

**Forces in Play:**
- **Weight of the Hanging Block:** Acts downward due to gravity and equals the mass of the block multiplied by gravitational acceleration (W = mg).
- **Tension in the String (T₁ and T₂):** The force exerted by the string on both blocks. If the pulley is frictionless and the string is massless, the tension throughout the string remains the same.

**Exploration:**
To analyze this system, assume the following:
- The string is inextensible and massless.
- The pulley is frictionless.
- The surface upon which T₂ rests is smooth to simplify calculations.

### Newton’s Second Law Application
1. **For the Hanging Block (T₁):**
- Apply Newton's second law \(T - mg = ma\).
2. **For the Block on the Surface (T₂):**
- If there's no friction, \(T = ma\).

### Calculation Steps
To solve for the acceleration \(a\) and tensions \(T₁\) and \(T₂\):
- Identify the masses of the blocks (m₁ for the hanging block, m₂ for the block on the surface).
- Set up the equations of motion.
- Solve for the unknowns using algebra.

By analyzing each component and the forces acting on them, students can better understand the dynamics of pulley systems and the interplay of different forces.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions