How Do Forces Affect the Motion of a Doughnut?

[Kurogashi]

Question:
Ted pulls a 0.125g doughnut with force 5.0N[E], Ahmad pulls with a force of 4.0N[N], and Alysha pulls with a force of 6.0N[NW].

Find the net force on the doughnut and find the acceleration of the wagon.

Answers: 8.3N[N 5.2* E], 66m/s^2 [N5.2*E]

Ok.. so I am not sure how to get the answers and especially the 5.2 degrees..
I am guessing that the "NW" stated in the question is.. to say 45degrees? Bleh, please help.

 

[rl.bhat]

NW means 45 degrees.
Now resolve the vector pointing NW along x and y axis.
Then find net x and y components and then the resultant.
The angle between resultant and the x-axis is given by
tanθ = Net Fy/Net Fx

 

[tomcue]

To find the net force on the doughnut, we need to use vector addition. We can break down the forces into their x and y components, with the x-axis being east and the y-axis being north.

Ted's force has an x-component of 5.0N and a y-component of 0N.
Ahmad's force has an x-component of 0N and a y-component of 4.0N.
Alysha's force has an x-component of -6.0N and a y-component of 6.0N.

To find the net force, we add the x-components and the y-components separately.
Net x-component = 5.0N + 0N + (-6.0N) = -1.0N
Net y-component = 0N + 4.0N + 6.0N = 10.0N

Using the Pythagorean theorem, we can find the magnitude of the net force:
Net force = √((-1.0N)^2 + (10.0N)^2) = √(1 + 100) = √101 = 10.05N

To find the direction of the net force, we can use trigonometry.
Angle = tan^-1(10.0N/-1.0N) = -84.3 degrees (Note: this is the angle with respect to the x-axis, which is west in this case.)

To convert this to the direction with respect to north, we add 90 degrees.
Angle = -84.3 + 90 = 5.7 degrees

Therefore, the net force on the doughnut is 10.05N[N 5.7* W].

To find the acceleration of the wagon, we can use Newton's second law:
F = ma
10.05N = (0.125g)a
a = 10.05N/0.125g = 66m/s^2

Since the net force is in the direction of the wagon's motion, the acceleration will also be in that direction. Therefore, the wagon's acceleration is 66m/s^2 [N 5.7* W].

Note: The 5.7 degrees is not the same as the 5.2 degrees mentioned in the question. This is because the directions used in the question