Find the tension?

Question

Find tension?
I asked this question about 40 mins ago, and I got the accelerations for both, but I cant get the tension force? I got 78.4 but the problem says that it isnt right, I dont know what it could be, I tried including g just incase but it said 186.2 was wrong too, any help?

An object with mass m1 = 3.00 kg, rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 8.0 kg, as shown in Figure P4.30. Find the acceleration of each object and the tension in the cable.

http://i165.photobucket.com/albums/u78/RLB31384/p4-30.gif

the acceleration is 7.127272727ms^2 for both

believe that its either done by doing 78.4-8*7.12727 = 501.759808

but im not sure if thats right, do I include g somewhere...

Answer 1

hey, i didn't get jow u got ur acceleration... now for what i think:

force acting on the 8kg object:
8*9.8 = 78.4N


now say, u're pulling the 8kg object down.. then u have the 3kg object resisting the motion..

now that force is : 3*9.8 = 29.4N

SO the tension is: 78.4-29.4= 49N

i think... if it's wrong, do tell me why.. i'm learning too

Answer 2

The mass of the system is M = m1 + m2 = 11 kg.

The only force acting on the system is the force of gravity (W) and it is acting along the cable only on the hanging mass. Thus, W = m2 g ~ 80 Newtons. (I'm rounding off the g for ease in calculation.)

Thus, the net force f = Ma = m2 g; so the a = (m2/M) g ~ (8/11) 10 ~ 8 m/sec^2. Since the "system" includes both masses, both objects are accelerating about 8 m/sec^2. (This is a bit high because I'm using g = 10 m/sec^2)

Now, the tension (T). Since both masses are keeping equidistant from each other, they are not accelerating relative to each other. The only way that can happen is for the forces on the cable to cancel out. Otherwise, one mass would be moving relative to the other.

The force on m1 is f1 = m1 a; it's the force pulling the second mass along at the same acceleration (a ~ 8 m/sec^2) as the entire system M. Thus, tension F = f1 = m1 a = 3 (8) ~ 24 Newtons.

You can do the math with the precise g and get the answers you're looking for. The important thing, though, is that you understand the physics.

First, both masses (M) make up the system. So we use the total of the two objects when considering f = Ma.

Second, the only force acting on the system (along the cable) is the force of gravity on m2. Thus W = m2 g. To be sure m1 has weight, but that weight is not acting along the cable; it is acting perpendicular to it so it has no bearing on the system's acceleration and tension along the cable.

Finally, as the two masses remain equidistant from each other, they are not accelerating relative to each other. Thus, the cable forces holding them together must add up to zero. So, by calculating the force on one mass, you automatically know the force on the other one is equal and opposite. Therefore, the tension can be no greater than the smaller of the two forces on the respective masses. That is, T = f1 = m1 a = 3(8) ~ 24 Newtons.