(Apparently, I'm not allowed to post URLs, but this question is better illustrated by a diagram, i39. tinypic. com/ 17e336. jpg)
<--P--[BOX A]<--Q--[BOX B]<--R--[BOX C]
There are three boxes attached together with string and being pulled across a frictionless surface. Box A has a mass of 2 kg, box B has a mass of 4 kg and box C has a mass of 4 kg. The strings are labelled P, Q and R respectively.
The force of tension for string P is 250 N. I have to find the force of tension for strings Q and R.
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On a system diagram of the entire system, I already found the acceleration (a = F/m = (250/10) = 25 m/s^2). This acceleration is the same for the whole system, right? But I don't know how to find the forces of tension for strings Q and R.
Any help?
Thanks.
Yes, the acceleration is for all of them.
The tension on each string is the mass following that string times the acceleration.
Then for FTQ (force of tension of string Q):
F=ma
=(8)(25)
=200 m/s^2
FTR
F=ma
=(4)(25)
=100 m/s^2
??
To find the force of tension for strings Q and R, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, we need to consider each box separately.
Let's first consider box B. The net force acting on box B is the tension in string P pulling it forward, minus the tension in string Q pulling it backward.
For box B:
Net force = Tension in string P - Tension in string Q
Since we know the mass of box B is 4 kg and the acceleration is 25 m/s^2, we can rewrite the equation using Newton's second law:
4 kg * 25 m/s^2 = Tension in string P - Tension in string Q
Now, let's consider box C. The net force acting on box C is the tension in string Q pulling it forward, minus the tension in string R pulling it backward.
For box C:
Net force = Tension in string Q - Tension in string R
Since we know the mass of box C is 4 kg and the acceleration is 25 m/s^2, we can rewrite the equation using Newton's second law:
4 kg * 25 m/s^2 = Tension in string Q - Tension in string R
Now we have two equations:
1) 4 kg * 25 m/s^2 = Tension in string P - Tension in string Q
2) 4 kg * 25 m/s^2 = Tension in string Q - Tension in string R
To solve for the tension in string Q, we can rearrange equation (1):
Tension in string Q = Tension in string P - 4 kg * 25 m/s^2
Substituting this value into equation (2), we have:
4 kg * 25 m/s^2 = (Tension in string P - 4 kg * 25 m/s^2) - Tension in string R
Simplifying the equation, we find:
Tension in string R = Tension in string P - 2 * 4 kg * 25 m/s^2
Plugging in the known values, we can calculate the force of tension for string Q and string R.