TeeterTotter Question?

Question

A child sits on one side of a teeter totter of length 8.00 m, a distance of 45.0 cm away from the end of the beam. The child has a mass of 23.7 kg. Her mother has a mass of 48.5 kg. How far away from her end does she have to sit in order for the teeter tooter to be exactly balanced?

I tried using the equation r2 = r1(m1/m2), but that did not work.

Thanks for any help.

Answer 1

So the length of the teeter totter is 8 m, therefore 4m on either side.
child sits .45 m awaw from end,
so i can say the child sits 3.55 m from the centre.
his mass his 23.7
so mass x distance from center = 23.7 kg x 3.55 m
thats = 84.135 kgm

take the mother now,
her mass is 48.5
for her to exactly cancel out her son's weight, she should sit at x m from center so that

Xm x 48.5 kg = 84.135 kgm
Xm = 1.734

so she should sit 1.734 m from the center
or you can say 2.265 m from her end

thats all there is to this problem!
hope i helped.

Answer 2

To solve this question you need to treat each person’s weight (of the child and the mother) as a torque force acting on the teeter-totter. Each torque wants to cause the teeter-totter to start rotating. In order for it to be balanced, you need to set the torques equal to each other, therefore there will be not net angular push.

Torque = Force * distance
You can see that at a larger distance or with a larger force the torque force becomes greater.
The force in question here is the weight (force due to gravity) of the child or of the mother and the distance is each person’s respective distance from the center of the teeter-totter.

Weight = mass * gravity
Where “gravity” is the gravitational acceleration the person experiences (9.81 m/s^2).


Child:
Weight = (23.7 kg) * (9.81 m/s^2)
Weight = 232.5 Newtons

Distance = ((Total Length of teeter-totter) / 2) - Distance to end
Distance = (4.00 meters - .45 meters)
Distance = 3.55 meters

Torque = (232.5 N) * (3.55 m)
Torque = 825.4 Newton meters


Mother:
Weight = (48.5 kg) * (9.81 m/s^2)
Weight = 475.8 Newtons

Distance = ?

Torque = 825.4 Newton meters
We know the mother’s torque must be equal to the child’s torque even though we don’t know where the mother is sitting yet.

Torque = Force * distance
Distance = Torque / Force
Distance = (825.4 Newton meters) / (475.8 Newtons)
Distance = 1.73 meters

So the mother must sit at a distance of 1 meter and 73 cm away from the center of the teeter-totter to balance the teeter-totter.

Answer 3

(4-0.45)*23.7 = x * 48.5

x being the distance of the mother to the center of the teeter.

As x = 1.735 m , the mother seats at 1.735 from the center, or
4-1.745 = 2.265 m from the end of her beam.

You need to work with distances to the center of the teeter, and use all distances in the same unit (m for instance).

Answer 4

That's because you got the distances wrong. The distances must all be converted to metres measured from the pivot point in the middle of the beam.

The answer you get using your equation will also be the distance from the pivot. You then need to work out the distance from the end.

Draw a diagram and mark the distances on it and you will see what is going on.