If a 100 kg adult sits on a first class lever 2.3 meters away from the axis of rotation...how far back do I need to sit (145 lbs) on the other side to balance the lever?
To balance the lever, you need to ensure that the torques on both sides of the lever are equal. Torque is calculated by multiplying the force applied by the distance from the axis of rotation.
In this case, the torque exerted by the 100 kg adult can be calculated using the formula: Torque = force x distance.
The force is the weight of the adult, which can be calculated as mass x acceleration due to gravity. The mass is given as 100 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
So the force exerted by the adult is 100 kg x 9.8 m/s^2 = 980 Newtons.
Now that we have the force, we can calculate the torque exerted by the adult. The distance from the axis of rotation is given as 2.3 meters. Therefore, the torque exerted by the adult is 980 N x 2.3 m = 2254 Nm.
To balance the lever, the torque exerted by your weight must be equal and opposite to the torque exerted by the adult. Your weight is given as 145 lbs. To convert this to Newtons, we need to multiply by the conversion factor 4.45 (1 lb = 4.45 N).
So your weight in Newtons is 145 lbs x 4.45 N/lb = 643.25 N.
To find the distance at which you need to sit on the other side of the lever, we rearrange the formula: distance = torque / force. Plugging in the values, we get: distance = 2254 Nm / 643.25 N ≈ 3.50 meters.
Therefore, to balance the lever, you need to sit approximately 3.50 meters away from the axis of rotation on the other side.