Question

Suppose you needed to raise a 205 kg mower a distance of 6.0 cm above the ground to change a tire. If you had a 1.9 m long lever, where would you place the fulcrum (in m) if your force was limited to 330 N? (Enter the minimum distance measured from your end of the lever.)

Answer 1

Recall the condition for rotational torque of an object,

Net torque = 0

The free body diagram representing the scenario is shown below

W is the weight of the mower

The point 0 is the pivot. Since the lever is in equilibrium, the net force about the pivot is zero

Taking the net torque about the pivot,

330r = W(1.9 - r) = mg(1.9 - r)

From the information given,

m = 205

g = acceleration due to gravity = 9.81

W = mg = 205 x 9.81 = 2011.05

Thus,

330r = 2011.05(1.9 - r) = 3820.995 - 2011.05r

330r + 2011.05r = 3820.995

2341.05r = 3820.995

r = 3820.995/2341.05

r = 1.63 m

The fulcrum would be placed at a distance of 1.63 m if the force was limited to 330N