Net Force on Log: Solving Using Cosine & Sine Laws

[mom2maxncoop]

Homework Statement

Two ropes are attached to a log that is floating in the water. A force of 80.0 N is applied to one rope and a force of 60.0 N is applied to the other rope, which is lying at an angle of 40° from the first rope. What is the net force on the log?

We know that the angle between the two known vectors is 140°.

Homework Equations

Cosine law:
c2=a2+b2-2abCosC

Sine Law:
sinA/a= SinB/b

The Attempt at a Solution

Cosine Law:
c²=a²+b²-2abCosC
c²=[(80.0)²+[60.0]²-2(80.0)x(60.0)cos140]
c=[80)²+(60)²-2(80)x(60)cos14]^½
c=131.346828
c=132 N

Now to find the angle between the resultnt force vector and the 80.0 N vector, use sine law

sinA/a = sinB/b = sinC/c

sinA/60.0 N = sin140°/132 N
sinA/60.0 N x 60.0 = sin140/132 x60.0
sinA =sin140/132 x 60.0
sinA = 0.292176186
A= sin$^{-}$0292176186


would that be correct??

 

[Doc Al]

Looks good. So what's your final answer for the angle?

 

[mom2maxncoop]

The answer I got was

Fnet= 132 N [17°counter clock-wise] from the original vector of 80.0N.

 

[Doc Al]

Looks good.

 

[rwisz]

I would like to provide some feedback and suggestions for your solution. Firstly, it is important to state the assumptions and simplifications made in the problem, such as assuming the log is stationary and neglecting any other forces acting on it. Additionally, it would be helpful to define the coordinate system used and label the forces and angles accordingly.

In terms of the solution, it is correct to use the cosine law to find the magnitude of the resultant force. However, it is important to note that the angle between the two known vectors is not 140°, but rather 180°-40° = 140°. This would change the values used in the cosine law calculation.

For the angle between the resultant force vector and the 80.0 N vector, it is not necessary to use the sine law. Instead, you can use the definition of the cosine function to find the angle. From your solution, it seems like you are trying to find the angle between the resultant force vector and the x-axis (which is not the 80.0 N vector). The correct angle to find would be between the resultant force vector and the 60.0 N vector.

Overall, your solution is on the right track but there are some minor errors that need to be corrected. Keep up the good work!