To loosen the lid on a jar of jam 8.9 cm in diameter a torque of 7.5 n·m must be applied to the circumference of the lid. if a jar wrench whose handle extends 13 cm from the center of the jar is attached to the lid, what is the minimum force required to open the jar?

Refer to the diagram shown below.

F =  the minimum force required for opening the lid
r = 8.9/2 = 4.45 cm = 0.0445 m
P =  the applied force, aplied at a distance of 13 cm = 0.13 m.

Because the required torque is 7.5 N-m, therefore
(0.13 m)*(P N) = 7.5 N-m
P = 57.6923 N

The equation for the lever requires that
0.13P = 0.0445F = 7.5
Therefore
F = 7.5/.0445 = 168.54 N

168.5 N