# How to find tension in strings pulling on carts.

## Homework Statement

3 carts are connected by strings. The first cart is 5kg, the second 2kg, and the third 8kg. A string is fixed at the front of the first cart is pulled with a force of 30 N. In the following problems be sure to illustrate your answers with the corresponding free body diagrams.

a. What is the acceleration of the train of carts?

b. What is the tension in the string connecting the first and second car?

c. What is the tension in the string connecting the second and third car?

## Homework Equations

Fnet = ma

I don't remember the equations to find tension

## The Attempt at a Solution

I figured out the acceleration easily:

Fnet = (m1 + m2 + m3)a
30 N = (15kg)a
a = 2 m/s ^2

The problem i'm having is I forget how to find the tension force in the strings.

Any help?

## The Attempt at a Solution

Drawing a FBD for each cart is THE FIRST STEP and is VERY IMPORTANT.

ok, so for the first one I have 30 N pulling it in one direction (let's say to the left). So then the tension Force (Ft) is pulling in the opposite direction, right? But this is where I get confused. I don't know how to find the magnitude of the tension force.

Try to use Fnet = ma for the FIRST cart.

so I have a force of 10 N pulling to the left?

Considering the first cart:

Let us keep the FBD in mind.

The first cart has 30N to the left and the tension T to the right. Hence Fnet in the direction of the acceleration is (30 - T).

using Fnet = ma (in the direction of the acceleration)
30 - T = 5 x 2

etc.

The same may be done for the other two carts. Always keep the FBD in mind.