Balance Beam: Solve + Explain Help

[Sunshine12]

Homework Statement

01"{
5. (12)A balance beam device comprised of a 200 cm long beam of unobtainium (no mass) ]
\]and a fulcrum located in the middle of the beam is balanced straight and level. At the right side of the beam system a mass of 30 kg is attached and at the other end of the beam system a mass of 25 kg is attached.
Find:

a) the torques acting on the system

b) the net torque and direction of rotation

c) Yippie the wonder dog, well beyond the prime of life, sees the problem of the unbalanced system with failing eyes. Yippie leaps up to the top of the fulcrum and after a less than stellar landing at the fulcrum point begins limping about on the left side of the fulcrum. The years have not been kind; our beloved Yippie has porked out to 25 kg (table orts you know). Help out, where must Yippie sit to bring the system into balance?

Homework Equations

The Attempt at a Solution

I missed this lecture and am absolutely not understanding this. Can someone please solve this + explain at each step?

 

[JHamm]

You'd do best to read up on torques, you'll be spending a while on this stuff and having a good understanding from the get go will put you miles ahead.

http://en.wikipedia.org/wiki/Torque

Try this video lecture (and any from this series if you're having troubles), they really are golden.
http://video.google.com/videoplay?docid=6480119270481031622

 

[Sunshine12]

You'd do best to read up on torques, you'll be spending a while on this stuff and having a good understanding from the get go will put you miles ahead.

http://en.wikipedia.org/wiki/Torque

Try this video lecture (and any from this series if you're having troubles), they really are golden.
http://video.google.com/videoplay?docid=6480119270481031622

i understand torque, i just don't understand how to balance these out and what not..i really need to see it solved to really get it x_x

 

[JHamm]

In that case why don't you give (a) a stab, you just need to calculate the torque from each weight (distance x force).

 

[asteriatic]

As a scientist, it is important to understand the physical principles behind any problem before attempting to solve it. In this case, the balance beam device is a classic example of a simple machine known as a lever. A lever works by using a fulcrum to balance the forces acting on either side of the lever. In this scenario, the fulcrum is located in the middle of the beam, and two masses (30 kg and 25 kg) are attached to either end of the beam.

To find the torques acting on the system, we will use the equation T = Fd, where T is the torque, F is the force, and d is the distance from the fulcrum. Since the beam is balanced, the net torque acting on the system must be zero. This means that the torques on either side of the fulcrum must be equal in magnitude and opposite in direction.

a) The torque on the right side of the beam can be calculated as follows:

T = (30 kg)(9.8 m/s^2)(100 cm) = 29400 Ncm

The torque on the left side of the beam can be calculated as follows:

T = (25 kg)(9.8 m/s^2)(100 cm) = 24500 Ncm

b) The net torque is found by subtracting the torque on the left side from the torque on the right side.

Net torque = 29400 Ncm - 24500 Ncm = 4900 Ncm

The direction of rotation will depend on which side has a greater torque. In this case, since the torque on the right side is greater, the beam will rotate clockwise.

c) To find the position where Yippie must sit to bring the system into balance, we can use the equation T = Fd again. We know that the net torque must be zero, so we can set the torques on either side of the fulcrum equal to each other.

Tleft = Tright

(Fleft)(dleft) = (Fright)(dright)

Since we know that Yippie's weight is 25 kg, we can set Fleft = 25 kg and solve for dleft.

25 kg(dleft) = (30 kg)(100 cm)

dleft = 120 cm

This means that Yippie must sit 120 cm from the fulcrum on the left side to balance out the 30 kg mass