# The tool at A is used to hold a power lawnmower 1

The tool at A is used to hold a power lawnmower blade stationary while the nut is being loosened with the wrench. If a force of 50 N is applied to the wrench at B in the direction shown, determine the moment it creates about the nut at C. What is the magnitude of force F at A so that it creates the opposite moment about C?

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

The moment at C which occurs because of the force at B can be calculated by multiplying the perpendicular force by the distance to point C. Remember that a force (or a component of a force) passing through the point of interest creates no moment. Refer to the image below:

The moment at C is:

$\circlearrowright M_C=(50\sin60^0)(0.3)=12.99$ N•m

(Remember, the distance from point C to B is 300 mm = 0.3 m)

To figure out the force F which creates an opposite moment at C equal to the moment created by the force at B, we can write the following:

$\circlearrowright M_C=0$

Since the force must create an opposite moment that cancels out the moment created by the force at B, the total moment created at point C must be 0. At point A, only the vertical component of force F will create a moment since the horizontal component will pass through point C. Thus:

$\circlearrowright M_C=0$

$0=-F(\dfrac{12}{13})(0.4)+12.99$

(Force F is negative because we assumed forces creating a clockwise moment to be positive)

$F=35.18$ N

$\circlearrowright M_C=12.99$ N•m
$F=35.18$ N