# What is the tension in the string?

• A_lilah
In summary, two blocks, 3.7 kg and 6.0 kg, are connected by a string and subjected to two external forces, FA = 13 N and FB = 24 N, both acting to the right. The tension in the string cannot be determined without additional information, such as the friction coefficients of the surfaces or the acceleration of the system.
A_lilah

## Homework Statement

3.7 kg block A and 6.0 kg block are connected by a string of negligable mass. Force FA = (13 N) acts on block A; force FB = (24 N) acts on block B. What is the tension in the string? (both force FA and FB are to the right)

fnet = ma

## The Attempt at a Solution

Block A FBD:
Weight force down of m*g = 36.297N
Normal force up (opposite of weight)
frictional force to the left = f1
FA to the right = 13N
Tension, T, to the right

Block B FBD:
Weight force down = 58.8N
Normal force up (opposite of weight)
frictional force to the right = f2
FB to the right = 24 N
Tension force, T, to the left

equations:
Fnet Ax = 3.7kg * a = 13N + T - f1
Fnet Bx = 6kg * a = 24N -T + f2
Fnet of A and B together = 9.7 kg * a = 37N + f2 -f1

Problem: four unknowns and only three equations...

One of those equations is extraneous, so you really just have 2 equations with 4 unknowns. If the surface is frictionless, f1 and f2 are 0; if friction is involved, the problem needs to state the friction coefficients, otherwise, you can't get a numeric answer. IF friction is involved, you made an error on the sign of f2..why did you have it as plus? (I'm guessing that the floor is horizontal and frictionless? If friction were presnt, the system might not move).

Based on the given information, the tension in the string can be calculated using the principle of equilibrium, which states that the net force on an object is equal to zero. In this case, we can set up two equations, one for each block, and solve for the tension.

For block A:

Fnet = ma
13 N + T - f1 = 3.7 kg * a

For block B:

Fnet = ma
24 N - T + f2 = 6.0 kg * a

We can also use the third equation, which represents the combined forces on both blocks:

Fnet = ma
37 N + f2 - f1 = 9.7 kg * a

Now, we have three equations and three unknowns (T, f1, f2), which can be solved using algebraic methods. Once we have the values for f1 and f2, we can plug them into one of the first two equations to solve for the tension, T.

Therefore, the tension in the string can be calculated by solving the system of equations and will depend on the values of f1 and f2, which are determined by the specific situation and the coefficients of friction.

## 1. What is tension in a string?

Tension is a force that is applied to an object through a string or other type of flexible material. It is the force that causes the string to be pulled tight and resist being stretched or broken.

## 2. How is tension measured?

Tension is typically measured in units of force, such as newtons or pounds. It can be measured using a variety of instruments, such as a spring scale or a tension meter.

## 3. What factors affect the tension in a string?

The tension in a string is affected by several factors, including the length and thickness of the string, the material it is made of, and the amount of force applied to it. Other factors can include the temperature and humidity of the environment, as well as the presence of any knots or bends in the string.

## 4. How does tension impact the behavior of a string?

Tension plays a crucial role in determining how a string will behave. For example, a higher tension will result in a higher pitch when plucked, while a lower tension will result in a lower pitch. Tension also affects the speed at which waves travel through a string, as well as its ability to transfer energy.

## 5. What are some common applications of tension in strings?

Tension in strings has many practical applications, such as in musical instruments, zip lines, and suspension bridges. It is also used in various forms of machinery, such as pulleys and conveyor belts, to transfer and control the movement of objects.

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