Calculating Work Done by a Force on a Coin

[dorkymichelle]

Homework Statement

A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates (2.2 m, 6.1 m) while a constant force acts on it. The force has magnitude 8.2 N and is directed at a counterclockwise angle of 108° from the positive direction of the x axis. How much work is done by the force on the coin during the displacement?

Homework Equations

W=FdCos a
a = angle between force and displacement
x²+y² = d²

The Attempt at a Solution

pt 1 = 0,0, pt 2 = 2.2m, 6.1m
using distance formula
displacement = square root (2.2)²+6.1²
d= 6.48
force = 8.2
and a = 108 degrees
so w = 8.2*6.48 *cos 108 = -16.42 J
I think the problem is that the angle between displacement and force is not really 108 and I am supposed to figure out where it is.. not I'm not sure where that's going..

edit , I just did tan b = 6.1/2.2
b = 70.167 degrees, being the angle between the displacement and pos x axis.
would the angle a, between force and displacement be angle of force - angle of displacement? 108-70 = 38 degrees.
and 38 degrees would be the angle that is put into the w = f*d equation?
I need someone to confirm because I'm on my last try on homework = /

 

[Berko]

yup. looks good. I'll do it quick here to make sure we both get the same answer. One sec..

I get 42 Joules (to 2 sig figs)