A 3 m long lever is used to lift a mass of 500 kg. If a force of 200 N is to be used to life the mass, then how far from the mass should the fulcrum be placed? Assume the mass and the force act at the ends of the lever.
To solve this problem, we can use the principle of moments, which states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
The moment of a force about a point is given by the equation:
Moment = Force × Distance
In this case, we have a 3 m long lever, a force of 200 N, and a mass of 500 kg. We need to find the distance from the fulcrum (or pivot point) where the mass should be placed. Let's call this distance x.
The moment created by the force is equal to the force multiplied by the distance from the fulcrum to the force. In this case, the force is 200 N, and the distance is 3 m - x. So, the moment created by the force is 200 N × (3 m - x).
The moment created by the mass is equal to the mass multiplied by the distance from the fulcrum to the mass. In this case, the mass is 500 kg, and the distance is x. So, the moment created by the mass is 500 kg × g × x, where g is the acceleration due to gravity (approximately 9.8 m/s²).
According to the principle of moments, the sum of the clockwise moments (mass moment) is equal to the sum of the anticlockwise moments (force moment). Therefore, we have the equation:
Mass moment = Force moment
500 kg × g × x = 200 N × (3 m - x)
Now, let's solve for x.
First, let's substitute the value for g:
500 kg × 9.8 m/s² × x = 200 N × (3 m - x)
Now, let's simplify the equation:
4,900 x = 600 - 200 x
4,900 x + 200 x = 600
5,100 x = 600
x = 600 / 5,100
x ≈ 0.1176 m
Therefore, the fulcrum should be placed approximately 0.1176 m or 11.76 cm away from the mass.