A mechanic applies a force of 42 Newtons straight down to a ratchet that is 0.59 meter long. What is the magnitude of the torque when the handle makes a 38° angle above the horizontal?

Answer 1

The downward force makes a 38° angle with the force normal to the Ratchet:

Let F_n be the force normal to the Ratchet

Let F be the force exerted straight down on the Ratchet

From Geometry: F= F_n cos 38° , and F_n = F / cos 38° = 42 N / cos 38° = 53.3 N

The Torque is T = F_n x Ratchet length = 53.3 N x 0.59 m = 31.45 N.m

Alternative Method:

The downward force makes a 52° angle with the horizontal:

Let F_n be the force normal to the Ratchet

Let F be the force exerted straight down on the Ratchet

From Geometry: F= F_n sin 52° , and F_n = F / sin 52° = 42 N / sin 52° = 53.3 N

The Torque is T = F_n x Ratchet length = 53.3 N x 0.59 m = 31.45 N.m