How Do You Solve a Physics Problem Involving Multiple Forces and Acceleration?

[Husker70]

Homework Statement

Three forces given, by F1=(-2.00i + 2.00j)N, F2=(5.00i - 3.00j)N, and F3=(-45.0i)N
act on an object to give it an acceleration of magnitude 3.75 m/s2.
(a) What is the direction of the acceleration?
(b) What is the mass of the object?
(c) If the object is initially at rest what is its speed after 10.0s?
(d) What are the velocity components after 10.0s?

Homework Equations

I added the forces together and get (-42.0i + 5.00j)
I found the hyp of the triangle x=43 and y=5 to be 42.3

The Attempt at a Solution

(a) Tan-1 (5/42) = 6.7 or 173 degrees
(b) m=F/A m= 42.3N/3.75m/s2 = 11.3kg

Am I doing this correct so far?
Thanks,
Kevin

 

[anathema]

Dear Kevin,

Your calculations for parts (a) and (b) are correct. For part (c), you can use the equation v = v0 + at, where v0 is the initial velocity (which is 0 m/s since the object is initially at rest), a is the acceleration (3.75 m/s2), and t is the time (10.0 s). This gives you a final velocity of 37.5 m/s.

For part (d), you can use the equation vf = vi + at, where vf is the final velocity (37.5 m/s), vi is the initial velocity (0 m/s), a is the acceleration (3.75 m/s2), and t is the time (10.0 s). This gives you the x-component of the velocity as 37.5 m/s and the y-component as 37.5 m/s.

Hope this helps!

 

[baba89]

Your solution looks correct so far. To verify, you can also use the Pythagorean theorem to find the magnitude of the acceleration, which should be 3.75 m/s^2. Additionally, for part (b), you could also use the formula F=ma to solve for the mass, which should also give you 11.3 kg. For part (c), you can use the formula v=at to calculate the final velocity after 10.0s. And for part (d), you can use the formula vf=vi+at to find the final velocity components in the x and y directions.