Help with problem associated with Newton II?

Question

2 loaded carts of mass 3kg and 4kg which are joined by a string are pulled by a spring balance along a frictionless surface. The reading on the spring balance (attached to the 4kg mass) is 14N.

a) What is the tension on the string?

No matter how I try, I can't get the answer of 6N.

Any help would be deeply appreciated. Thanks!

Answer 1

The spring balance is attached to the 4kg mass which means the string is pulling the 3kg mass. Therefore, only the 3kg mass is actually causing tension in the string.

Firstly you'll have to consider both carts and then you look at just the 3kg mass.

Newton's 2nd law states F=ma

So what you'll need to do first is work out the acceleration of the carts. You're told the force is 14 N and the mass is 4+3=7kg (both carts combined since the spring balance is pulling both)

rearranging gives a=14/7 =2m/s²

so now that you know the acceleration you can work out the tension in the string.

Still using newtons second law T=ma (where T = tension force in string)

Since the string is only pulling the 3kg force you only put that into the equation.

Therefore T=3*2 = 6N

Answer 2

Reading of spring balance is equal to the tension in the spring of the spring balance.

Then tension in spring = 14 N

Take the two carts + string connecting them as system.

Mass of system = 3kg + 4kg = 7 kg (string's mass is negligible)

Tension in spring is the only external force on the system.

Acceleration a = force/mass = 14/7 m/s^2

Or a = 2m/s^2

Consider 3kg mass as the sysetm.

Force = mass*acceleration = 3*2 = 6 N

Tension in the spring is the only external force on 3kg mass.

Therefore, tension in the string = 6 N