A 15 cm wrench is used to screw in a bolt. If 30 n of force is applied to it at a 45 degree angle, how much torque is applied? (Round to the nearest tenth)

3.18 Nm

Explanation:

Given that:

Radius (r) = 15cm = 15/100 = 0.15m

θ = 45°

Applied force (F) = 30 N

The Torque can be obtained using the relation :

T = rF * sinθ

T = 0.15 * 30 * sin(45)

T = 0.15 * 30 * 0.7071067

T = 3.18198015

T = 3.18 Nm

we need to know the time interval during which the force acts. impulse of force = momentum change

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west