How Do You Calculate Acceleration with Vector Forces in Physics?

[frankfjf]

Alright, this is the problem:

Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-31, with F1 = 31 N, F2 = 34 N, F3 = 27 N, angle 1 = 27°, and angle 3 = 52°. What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction relative to the positive direction of the x axis?

I'm trying to understand how to apply Fnet = ma here.

I tried getting the components for the magnitudes 31, 34, and 27, then dividing the net components for x and y by the mass, but that doesn't give the correct answer. What am I doing wrong?

 

[nrqed]

Alright, this is the problem:

Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-31, with F1 = 31 N, F2 = 34 N, F3 = 27 N, angle 1 = 27°, and angle 3 = 52°. What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction relative to the positive direction of the x axis?

I'm trying to understand how to apply Fnet = ma here.

I tried getting the components for the magnitudes 31, 34, and 27, then dividing the net components for x and y by the mass, but that doesn't give the correct answer. What am I doing wrong?

Give your results.

You must find the x and y components of the three forces, $$F_{1x}, F_{1y}, etc$$ and then use $$a_x= {F_{1x} +F_{2x} +F_{3x} \over 2}$$ and the same for the y direction.

Pat

 

[frankfjf]

My results are 14.1i + 27.6j for F1, 34j for F2, and 21.3i + 16.6j for F3.

 

[frankfjf]

However, 35.4/2 does not give a correct answer for the horizontal component of a..

 

[frankfjf]

Would it be possible to be linked to an example problem involving this sort of thing? My textbook does not do a very good job of this.

 

[nrqed]

However, 35.4/2 does not give a correct answer for the horizontal component of a..

?? Don't you mean 35.4/120?
(the mass of the asteroid is 120 kg, right?)

Your components are right, assuming that the ansgles are given clockwise with respect to the vertical direction...

 

[frankfjf]

Sorry, my mistake. Dividing 35.4/120 does not give the correct answer for some reason.

 

[nrqed]

Sorry, my mistake. Dividing 35.4/120 does not give the correct answer for some reason.

And you are sure that all the angles are measured clockwise from the y axis? Also, the second force is in the positive y direction, right?

can you post the answers for a_x and a_y they give, maybe I will be able to see what they did.

 

[frankfjf]

Figured it out. The angles were not entirely right. It's my fault since the problem comes with a diagram, and after observing the 3 vectors, pretty much the problem was that the 52 degree angle is negative since it's in the 4th quadrant in the picture. Thanks for your help nrged.