Work Through a Displacement At An Angle

[mircobot]

Homework Statement

Find the work done when a force of 65 N acting at an angle of 170° from the x-axis is applied to an object that moves through a displacement of 2.2 m at an angle of 30°.

Homework Equations

W = Fcos$$\Theta$$d

where d is the distance moved in the direction of the force.

The Attempt at a Solution

I know I am slipping on my distance. The distance the object is traveling in the direction of the force is 2.2 m multiplied by the difference in the angles
W = ( 65 N ) * cos( 170° ) * ( 2.2 m ) * cos( 150° )

Obviously this is wrong, I don't understand how to find the distance part of the equation.

 

[mircobot]

Nevermind, I completely forgot that work is a scalar quantity and that obviously means it results from a dot product. I solved it...

I just found the vectors of the force and direction, and found their dot product.

 

[ogb p]

I would first clarify the problem by asking for more information. What is the direction of the displacement in relation to the x-axis? Is it in the same direction or opposite direction as the force? This will help determine the correct distance to use in the equation.

Assuming the displacement is in the same direction as the force, we can use the formula W = Fd cosθ, where d is the component of the displacement in the direction of the force. In this case, the component of the displacement in the direction of the force can be found by using the given angle of 30° and the total displacement of 2.2 m.

d = 2.2 m * cos(30°) = 1.9 m

Now we can plug in the values to find the work done:

W = (65 N) * (1.9 m) * cos(170°) = -191.7 J

Note that the negative sign indicates that the work is done in the opposite direction of the displacement, which makes sense since the force and displacement are at an angle of 170°. This means that the work done is negative, indicating that energy is being taken away from the object rather than added to it.

In conclusion, it is important to carefully consider the direction and magnitude of displacement when calculating work done at an angle. Additional information may be needed to accurately solve the problem.