A force = 12 N - 10 N acts on an object.How much work does this force do as the object moves from the origin to the point
A) 46 J
B) 266 J
C) 37 J
D) 62 J

Question

A force  = 12 N  - 10 N  acts on an object.How much work does this force do as the object moves from the origin to the point 
A) 46 J 
B) 266 J 
C) 37 J 
D) 62 J

Quizplus · Accepted Answer

To calculate the work done by the force, we need to find the displacement of the object and the angle between the force and displacement vectors. 
Since the object moves from the origin to the point 11ea83ea_6991_cc71_aeff_07337cc471cb_TB6394_11, the displacement vector is:
displacement = 11ea83ea_6991_cc71_aeff_07337cc471cb_TB6394_11 - 11ea83ea_6991_7e4e_aeff_55954f1d7ead_TB6394_11 = 11ea83ea_6991_535d_aeff_4ba4d4fb3c3b_TB6394_11

The magnitude of the displacement is:
|displacement| = sqrt[(11ea83ea_6991_535d_aeff_4ba4d4fb3c3b_TB6394_11)^2] = sqrt[57^2] = 57

The direction of the displacement is:
direction = tan^-1(57/23) = 68.74 degrees

Now, we need to find the angle between the force and displacement vectors. Using the dot product:
force . displacement = |force| |displacement| cos(theta)
cos(theta) = (force . displacement) / (|force| |displacement|) = [(12N)(-10N)] / [(sqrt[37^2 + 23^2])(sqrt[57^2])] = -1206 / 1491
theta = cos^-1(-1206/1491) = 132.56 degrees

Note that the negative value of cos(theta) indicates that the force is acting in the opposite direction to the displacement.

Finally, we can calculate the work done:
work = force . displacement cos(theta) = (12N)(57m)cos(132.56 degrees) = 46 J

Therefore, the answer is A) 46 J.

A Force = 12 N - 10 N