a lever is 5 m long. The distance from the fulcrum to the weight to be lifted is 1 m. If a 3000 N rock is to be lifted, how much force must be excerted on the lever?
F1*d1=F2*d2
F1=3000 d1 is 1m
F2=? d2 is 4m
solve for F2
750N
To calculate the force that must be exerted on the lever, we can use the principle of moments. The principle of moments states that the moment exerted by a force about a pivot point is equal to the product of the force and its distance from the pivot point.
In this case, the distance from the fulcrum to the weight (1 m) is shorter than the distance from the fulcrum to the point where the force is applied (unknown). Let's denote the force exerted on the lever as F.
According to the principle of moments, the moment exerted by the weight about the fulcrum is equal to the moment exerted by the force about the fulcrum.
Moment exerted by the weight = Moment exerted by the force
(3000 N) * (1 m) = (F) * (5 m)
Rearranging the equation, we can solve for F:
F = (3000 N * 1 m) / 5 m
F = 600 N
Therefore, in order to lift the 3000 N rock with a lever 5 m long and a distance of 1 m between the fulcrum and the rock, a force of 600 N must be exerted on the lever.
To determine the amount of force that must be exerted on the lever, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments must equal the sum of the counterclockwise moments.
In this case, the moment of force exerted by the rock (clockwise moment) must be equal to the moment of force exerted by the force applied on the lever (counterclockwise moment). The moment of a force is given by the formula:
Moment = force × distance
Let's assign variables to the given values:
Force exerted by the rock (clockwise moment) = FR
Force exerted on the lever (counterclockwise moment) = FL
Distance from the fulcrum to the weight to be lifted = dR = 1 m
Length of the lever = l = 5 m
Weight of the rock = W = 3000 N
Using the principle of moments, we can set up the equation:
FR × dR = FL × l
Substituting in the given values:
FR × 1 m = FL × 5 m
Simplifying the equation, we can isolate the unknown (FL):
FL = (FR × dR) / l
Now we can substitute the weight of the rock (3000 N) for the force exerted by the rock (FR) and solve for the force exerted on the lever (FL).
FL = (3000 N × 1 m) / 5 m
FL = 600 N
Therefore, a force of 600 Newtons must be exerted on the lever in order to lift the 3000 Newton rock.