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.

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To solve this problem, we can use the concept of moments, also known as torque. Torque is the tendency of a force to rotate an object about an axis, and it depends on the magnitude of the force and the distance from the axis of rotation.

Let's start by understanding the problem. We have a lever of length 3 m, and we need to find the distance at which the fulcrum should be placed from the mass. The force used to lift the mass is 200 N, and the mass itself is 500 kg.

The torque exerted by the force can be calculated using the formula:

Torque = Force x Distance

In this case, the force is 200 N, but we need to calculate the distance from the fulcrum. Let's assume this distance as 'x' meters.

Now, let's break down the forces exerted on the lever. The force of 200 N acts at one end of the lever, and we'll call this end point A. The mass of 500 kg acts at the other end of the lever, and we'll call this end point B. The fulcrum is placed at some distance x from point A.

To have rotational equilibrium, the total torque on the system must be zero. This means that the torques exerted by the two forces must balance each other out.

The torque exerted by the 200 N force at point A is given by:

Torque (force at A) = 200 N x (3 m - x) -- The distance from point A to the fulcrum is 3 m - x, as the fulcrum is placed at a distance of x from point A.

Similarly, the torque exerted by the mass at point B is given by:

Torque (mass at B) = 500 kg x 9.8 m/s^2 x x -- The force due to the weight of the mass is given by mass x gravity, and the distance from point B to the fulcrum is x.

For rotational equilibrium, both torques must be equal:

200 N x (3 m - x) = 500 kg x 9.8 m/s^2 x x

Simplifying the equation:

600 m N - 200 N x = 4900 kg m/s^2 x

Rearranging the equation:

200 N x + 4900 kg m/s^2 x = 600 N m

Combining like terms:

5100 kg m/s^2 x = 600 N m

Finally, solving for x:

x = 600 N m / 5100 kg m/s^2

x ≈ 0.118 m

Therefore, the fulcrum should be placed approximately 0.118 meters (or 11.8 cm) from the mass in order to lift it using a force of 200 N with a 3 m long lever.