A man uses a crowbar 1.5 meter long to lift a rock weighing 600 newton. If the fulcrum is 0.50 meter from the end of the bar touching the rock, how much effort must the man apply?
Take moments about the fulcrum and equate to zero. Solve for F=effort.
on the load side:
force = 600N
distance from fulcrum= 0.5 m
On the effort side:
force = F N
distance from fulcrum= 1.5m - 0.5 m = 1 m.
Moment equals force time distance from fulcrum, clockwise positive.
To calculate how much effort the man must apply to lift the rock using the crowbar, we can use the formula for a lever:
Effort x Effort Arm = Load x Load Arm
In this case, the Load is the weight of the rock, which is 600 Newton, and the Effort Arm is the distance from the fulcrum to the point where the man applies the effort (unknown). The Load Arm is the distance from the fulcrum to the end of the bar touching the rock, which is 0.50 meter. Given that the length of the crowbar is 1.5 meters, we can calculate the Effort Arm.
Load x Load Arm = Effort x Effort Arm
600 N x 0.50 m = Effort x (1.5 m - 0.50 m)
300 N = Effort x 1 m
Therefore, the man must apply an effort of 300 Newton to lift the rock with the crowbar.
To find how much effort the man must apply, 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.
In this case, the clockwise moment is produced by the weight of the rock, and the anticlockwise moment is produced by the effort applied by the man.
The moment of an object is calculated by multiplying the force applied by the perpendicular distance to the fulcrum. So, we can calculate the moments as follows:
Clockwise moment (due to the weight of the rock):
Moment(clockwise) = weight of the rock * distance from the fulcrum to the rock
= 600 N * 0.50 m
= 300 N∙m
Anticlockwise moment (due to the effort applied by the man):
Moment(anticlockwise) = effort applied by the man * distance from the fulcrum to the man
= effort applied by the man * (total length of the crowbar - distance from the fulcrum to the rock)
= effort applied by the man * (1.5 m - 0.50 m)
= effort applied by the man * 1.0 m
According to the principle of moments, these two moments are equal:
Moments(clockwise) = Moments(anticlockwise)
300 N∙m = effort applied by the man * 1.0 m
To solve for the effort applied by the man:
effort applied by the man = 300 N∙m / 1.0 m
= 300 N
Therefore, the man must apply an effort of 300 newtons to lift the rock using the crowbar.