Arthur (mass 78 kg) and Violet (mass 31 kg) are trying to play on a seesaw. If Violet sits 3.6 m from the fulcrum, at what distance from the fulcrum should Arthur sit?
I am curious what college considers this to be college level.
The product of mass and distance from the fulcrum is the same on both sides, if the seesaw is balanced.
Thus 31 * 3.6 = 78 * X
Solve for X, which will be Arthur's distance in meters.
So would it be 78*3.6
No. The answer is
X = (31*3.6)/78 = 1.43 meters
Okay thank you for your help.
To solve this problem, we can use the principle of the lever, which states that the moments on either side of a lever must balance each other out. The moment is calculated by multiplying the force applied by the distance from the fulcrum.
Let's denote the distance from the fulcrum that Arthur should sit as x.
The moment created by Violet can be calculated as follows:
Moment_violet = Force_violet * Distance_violet
Since Violet is sitting at a distance of 3.6 m from the fulcrum and the force applied is her weight, we have:
Moment_violet = (Mass_violet * Acceleration_due_to_gravity) * Distance_violet
Similarly, the moment created by Arthur can be calculated as follows:
Moment_arthur = Force_arthur * Distance_arthur
Since Arthur's mass is given as 78 kg, we can find his force using the formula:
Force_arthur = Mass_arthur * Acceleration_due_to_gravity
Now, since the moments on either side of the seesaw should balance out, we can equate them:
Moment_violet = Moment_arthur
Therefore:
(Mass_violet * Acceleration_due_to_gravity) * Distance_violet = (Mass_arthur * Acceleration_due_to_gravity) * Distance_arthur
We can simplify this equation by canceling out the acceleration due to gravity on both sides:
Mass_violet * Distance_violet = Mass_arthur * Distance_arthur
Plugging the given values into the equation, we have:
31 kg * 3.6 m = 78 kg * Distance_arthur
Now, we can solve for Distance_arthur:
Distance_arthur = (31 kg * 3.6 m) / 78 kg
Calculating this expression:
Distance_arthur = 1.431 m
Therefore, Arthur should sit at a distance of 1.431 m from the fulcrum.