A 4kg object is subjected to two forces, F1=2Ni-3Nj, and F2=4Ni-11Nj. The object is at rest at the origin at t=0.
What is the objects acceleration? I know you use F=m*a
Do you add the two F vectors together & take the square root to find the sum of F?
ex: Fnet=6Ni-14Nj & then sqrt(6^2+14^2)=12.5N
A = F/m
A = (F1+F2)/4
F1+F2 = 6 i - 14 j as you said
so
A = (3/2) i - (7/2) j
sure if you want the magnitude go ahead and use 12.5/4 but it just said find the acceleration which is the vector A
it looks right to me. just plug in 12.5N and 4kg into the formula and solve for acceleration.
Thanks guys!
How did you manage to get 12.5N? because sqrt(6^2+14^2) = 15.2 N. Unless you just got the numbers mixed up
Well, it seems like you're on the right track, but there's a slight twist here. To find the net force, you indeed need to add the two force vectors F1 and F2 together. So, adding 2Ni-3Nj and 4Ni-11Nj gives you a net force of 6Ni-14Nj, just like you said.
However, to find the magnitude of the net force, you don't need to take the square root. Instead, you can just find the magnitude using good old Pythagoras' theorem. So, the magnitude of the net force is √((6^2) + (-14^2)) ≈ 15N (approximately).
Now, since you know that F = m * a, and the object has a mass of 4kg, you can rearrange the equation to solve for the acceleration: a = F / m = 15N / 4kg ≈ 3.75 m/s².
So, the object's acceleration is approximately 3.75 m/s². Now, make sure you hold on tight to your clown nose because this physics stuff can be a wild ride!
To find the object's acceleration, you can indeed use the equation F = m * a. To apply this equation vectorially, you need to consider the individual components of the forces and acceleration.
Given that the object is subjected to two forces, F1 = 2Ni - 3Nj and F2 = 4Ni - 11Nj, you can find the net force acting on the object by adding the individual force components:
Fnet = F1 + F2 = (2Ni - 3Nj) + (4Ni - 11Nj) = 6Ni - 14Nj.
Now, you need to find the object's acceleration by dividing the net force by the mass (Fnet = m * a):
6Ni - 14Nj = 4kg * (a).
To find the magnitude of the acceleration (|a|), you can calculate the square root of the sum of the squares of the components:
|a| = sqrt((6^2) + (-14)^2) = sqrt(36 + 196) = sqrt(232) ≈ 15.23 m/s^2.
Therefore, the object's acceleration is approximately 15.23 m/s^2 in the opposite direction of the y-axis (negative j-direction), based on the negative j-component (-14Nj) of the net force.