. A 90cm uniform lever has a load of 30N suspended at 15cm from one of its ends. If the fulcrum is at the centre of gravity, calculate the force that must be applied at its other end to keep it horizontal
45 F = 30*(45-15)
20
To calculate the force that must be applied at the other end of the lever to keep it horizontal, we can use the principle of lever balance.
The principle of lever balance states that the sum of the moments on one side of a lever is equal to the sum of the moments on the other side of the lever.
In this case, the load of 30N is suspended at 15cm from one end of the lever. The fulcrum is at the center of gravity, so the distance from the fulcrum to the load is also 15cm.
Let's call the force that needs to be applied at the other end of the lever F.
According to the principle of lever balance, the moment on one side of the lever is equal to the moment on the other side of the lever. Mathematically, this can be expressed as:
Force x Distance = Load x Distance
F x 90cm = 30N x 15cm
Now we can solve for F:
F = (30N x 15cm) / 90cm
F = 5N
Therefore, the force that must be applied at the other end of the lever to keep it horizontal is 5N.
To calculate the force that must be applied at the other end of the lever to keep it horizontal, we can use the principle of moments. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
In this case, since the fulcrum is at the center of gravity, the lever will be in equilibrium. We can choose any point to calculate the moments, but for simplicity, let's choose the fulcrum as the point.
Let's denote the force at the other end (the effort force) as F. The load at a distance of 15cm from the fulcrum creates a clockwise moment, while the effort force at a distance of 45cm from the fulcrum creates an anticlockwise moment. The length of the lever is 90cm, so the distance between the load and effort force is 90cm - 15cm - 45cm = 30cm.
According to the principle of moments, we can set up the following equation:
(clockwise moment) = (anticlockwise moment)
Load x Load distance = Effort force x Effort force distance
30N x 15cm = F x 30cm
Now, we can solve this equation for F (the effort force).
30N x 15cm = F x 30cm
450 Ncm = 30 Fcm
Dividing both sides by 30cm:
15N = F
Therefore, the force that must be applied at the other end of the lever to keep it horizontal is 15N.