As shown in the figure below, two masses m1 = 4.20kg and m2 which has a mass 50.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.20m, use energy content to determine the following. (a) speed v of the masses m/s (b) magnitude of the tension T in the cord N
Kinematics
A machine is a device that accepts energy in some available form and utilizes it to do a type of work. Energy, work, or power has to be transferred from one mechanical part to another to run a machine. While the transfer of energy between two machine parts, those two parts experience a relative motion with each other. Studying such relative motions is termed kinematics.
Kinetic Energy and Work-Energy Theorem
In physics, work is the product of the net force in direction of the displacement and the magnitude of this displacement or it can also be defined as the energy transfer of an object when it is moved for a distance due to the forces acting on it in the direction of displacement and perpendicular to the displacement which is called the normal force. Energy is the capacity of any object doing work. The SI unit of work is joule and energy is Joule. This principle follows the second law of Newton's law of motion where the net force causes the acceleration of an object. The force of gravity which is downward force and the normal force acting on an object which is perpendicular to the object are equal in magnitude but opposite to the direction, so while determining the net force, these two components cancel out. The net force is the horizontal component of the force and in our explanation, we consider everything as frictionless surface since friction should also be calculated while called the work-energy component of the object. The two most basics of energy classification are potential energy and kinetic energy. There are various kinds of kinetic energy like chemical, mechanical, thermal, nuclear, electrical, radiant energy, and so on. The work is done when there is a change in energy and it mainly depends on the application of force and movement of the object. Let us say how much work is needed to lift a 5kg ball 5m high. Work is mathematically represented as Force ×Displacement. So it will be 5kg times the gravitational constant on earth and the distance moved by the object. Wnet=Fnet times Displacement.
As shown in the figure below, two masses m1 = 4.20kg and m2 which has a mass 50.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.20m, use energy content to determine the following.
(a) speed v of the masses m/s
(b) magnitude of the tension T in the cord N
![### Simple Pulley System
#### Description:
This diagram illustrates a simple pulley system used in classical mechanics to study the forces and motion involved. The system consists of two masses, \( m_1 \) and \( m_2 \), connected by a string that passes over a frictionless pulley.
#### Components of the diagram:
1. **Pulley:**
- Positioned at the top center of the diagram.
- Assumed to be frictionless, meaning it does not resist the motion of the string passing over it.
2. **String:**
- Connects the two masses and passes over the pulley.
- Assumed to be light and inextensible, meaning its mass is negligible, and it does not stretch.
3. **Masses:**
- \( m_1 \): On the right side, hanging downward.
- \( m_2 \): On the left side, also hanging downward.
- These masses are connected through the string on either side of the pulley.
4. **Distance \( h \):**
- Represents the vertical distance between mass \( m_1 \) and the reference ground level.
- Indicated by a dashed line vertically aligned with \( m_1 \).
#### Explanation:
- When released, the masses \( m_1 \) and \( m_2 \) will accelerate due to the force of gravity.
- If \( m_1 \) is heavier (has a greater gravitational force), \( m_1 \) will move downward, pulling \( m_2 \) upward.
- Conversely, if \( m_2 \) is heavier, it will move downward, pulling \( m_1 \) upward.
- The acceleration of the masses depends on the difference in their weights and can be analyzed using Newton's Second Law.
#### Equations:
For such a system, the accelerations and tensions can be described using the following equations of motion:
\[ m_1 g - T = m_1 a \]
\[ T - m_2 g = m_2 a \]
where:
- \( g \) is the acceleration due to gravity,
- \( T \) is the tension in the string,
- \( a \) is the acceleration of the masses.
By solving these equations simultaneously, you can determine the acceleration \( a \) and the tension \( T \) in the string.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81610fbc-71d4-4f51-a970-c974c7e9c894%2F48ed1f74-7495-4731-b6c8-f1d5c8265c2f%2Fy0ybx38_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
