Question #dfa0b

2 Answers
Dec 23, 2017

The correct answers are d and f.
The moment or torque is #0.02"Nm"# clockwise.
The arm is #4.9"cm"#.

Explanation:

The torque (or moment of force, angular force) is given by the formula
#vecM=vecr xx vecF#
where #vecr# is a vector from the pivot point to the location of the force (in this case from A to B), #vecF# is that force (in this case #vecW#).

This means the value of torque is
#M=rWsin(theta)#
where #theta# an angle beetwen vectors and direction is determined by right hand rule.
#theta=180^@-105^@=75^@# Actually this doesn't matter, since #sin(75^@)=sin(105^@)#

Extend the line of #vecW# and draw a line through A perpendicular to it.
copied from above
This is equivalent to placing brackets like this
#M=W(rsin(theta))#

The segment labeled "y cm" is called arm. Its length is #rsin(theta)=5.1"cm"*0.966=4.926"cm"~~4.9"cm"# (f)

#M=0.33"N" * 4.9"cm"=1.62"N" * "cm"=0.0162"Nm"~~0.02"Nm"# (b,d)

#color(red)("Remember about units")#

The torque is clockwise for reasons obvious to me (The force is pulling right side down, so it will move down) (d)

Alternative method

Break #vecW# down to parallel and perpendicular component.
copied from above
Parallel component #vec(F_2)# doesn't produce torque.
#vec(F_1)# is perpendicular to #vecr#, so
#M=rF_1#

This is equivalent to placing brackets like this
#M=r(Wcos(theta))#

One more method

#M=rWsin(theta)#

#r=5.1"cm"#, #W=0.33"N"# and #theta=75^@#

If all values are known, we can just calculate #sin(theta)# and multiply #rWsin(theta)#.

Dec 23, 2017

I agree with Voyager1: d and f.

Explanation:

I have one more method for calculating torque to add to the discussion.

Referring to my Physics book (by Resnick Halliday), the formula for Torque uses a vector cross product. To explain the vector cross product for the general case, my book says:

# vec C = vec A xx vecB = |A|*|B|*sinphi #

where #phi# is the angle between #vec A " and " vecB# measured in the manner that yields a value between #0^@ " and "180^@#.

When it discussed torque, my book defines it as
# vectau = vecr xx vecF#

Plugging in the data

# vectau = vecr xx vecF = 0.051 m*0.33 N*sin105^@ ~= 0.02 Nm#

I hope this helps,
Steve