System of equations with acceleration and tension

If so, you can use the equation T=Iα to find the angular acceleration of the pulley, and then use that to find the linear acceleration of the descending mass using the equation a=rα. Additionally, you can use the equation T=ma to find the tension in the string connecting the mass to the pulley. This will give you a system of equations with two unknowns (a and T) that you can solve to find the desired values. In summary, to find the linear acceleration of the descending mass and the tension in the string connecting it to the pulley, you can use the equations T=Iα, a=rα, and T=ma to create a system of equations and solve for the unknowns.
  • #1
Bob Rudd
2
0

Homework Statement


So there is a pulley with 1 mass hanging from it. The string is wrapped around and one end is taped to the pulley so that only one end of the string hangs from the pulley. There is a mass of 100 grams attached to that string. Create a system of equations to find linear acceleration of the descending mass and the tension in the string connecting the mass to the disk.

Homework Equations


F=ma

The Attempt at a Solution


The first equation would be T=mg-ma because the body is falling downward. How would i find the other equation with T and a to help me create a system of equations
 

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  • #2
Do you have any information about the pulley?
 

FAQ: System of equations with acceleration and tension

What is a system of equations with acceleration and tension?

A system of equations with acceleration and tension is a set of equations that relate the acceleration and tension of one or more objects in a physical system. These equations are used to solve for unknown values such as velocity, displacement, or force.

How do you solve a system of equations with acceleration and tension?

To solve a system of equations with acceleration and tension, you must first identify the variables involved and set up the equations based on known values and physical laws. Then, you can use algebraic methods such as substitution or elimination to solve for the unknown variables.

What are some real-life applications of systems of equations with acceleration and tension?

Systems of equations with acceleration and tension are commonly used in physics and engineering to model and solve problems related to motion, forces, and energy. Some real-life applications include analyzing the motion of objects on inclined planes, calculating the forces on a pulley system, and designing structures such as bridges or roller coasters.

What are the key variables in a system of equations with acceleration and tension?

The key variables in a system of equations with acceleration and tension include acceleration (a), tension (T), mass (m), force (F), and displacement (d). These variables are related through physical laws such as Newton's laws of motion and Hooke's law for springs.

What happens to the system of equations when the acceleration or tension changes?

When the acceleration or tension changes in a system of equations, the values of the other variables may also change. This is because acceleration and tension are interconnected with other variables through physical laws. Therefore, to solve for unknown values, the equations must be adjusted accordingly to account for the changes in acceleration or tension.

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