Final answer:
To lift a rock with the largest possible force using a lever, apply the lever principle, which states the anticlockwise and clockwise moments must balance. For the provided example, a fulcrum should be placed 0.49 meters from the point where a 300 N force is applied to lift a 250-kg mower with a 2.0-m long lever.
Step-by-step explanation:
To calculate how far from the rock you should place the fulcrum so that the largest force is just sufficient to lift the rock, you use the principle of moments, or the lever principle. This states that for a lever in equilibrium, the anticlockwise moment must equal the clockwise moment. The moment is given by the force times the distance from the fulcrum.
In the case of raising a 250-kg mower 6.0 cm above the ground using a 2.0-m long lever with a limited force of 300 N, you would calculate the distance from the fulcrum based on the equation:
Force × Distance on one side = Weight of the object × Distance on the opposite side.
First, convert the weight of the mower into Newtons by multiplying the mass (250 kg) by the acceleration due to gravity (approximately 9.81 m/s²). This gives us the weight:
Weight (W) = mass (m) × gravity (g)
= 250 kg × 9.81 m/s²
= 2452.5 N.
Using the lever principle, you set up the equation with the distances as the variables to solve for:
300 N × distance from the fulcrum (x) = 2452.5 N × 0.06 m,
where x is the distance from the fulcrum where you should apply the 300 N force. Solving for x gives:
x = (2452.5 N × 0.06 m) / 300 N
= 0.49 m.
Therefore, the fulcrum should be placed 0.49 meters from the end where the force is applied to lift the 250-kg mower.