Only two forces act on an object (mass = 4.00 kg), as in the drawing. Find the magnitude and direction (relative to the x axis) of the acceleration of the object.
Ftotal=Sqrt(60^2+40^2)=72.11(N)
Angle=tan-1(60/40)= 56.3° (How did you get 56.3°)
a= F/m=72.11/4=18(m/s/s)
The correct answer is 18.0 m/s2, 56.3° above the +x axis. I was wondering how did you get 56.3°? Please show your work
3 answers
α=arctan(Fy/Fx)=arctan(60/40)=arctan 1.5=56.3°
im 9 years late but basically u are given the x and y component of the force , x being 40N and y being 60N. And you can form a right triangle, by connecting the tail of the 40N to the tip of the 60N, and that forms the hypotenuse of the right triangle. Apply the pythagorean theorem to find the net force (which is sum of the forces), being 20 root 3. now, to find the angle, you are finding the angle that 40N and 20 root 3 form. Think about why. Since you want to find how much angle UP the positive x-axis, that's why you would want to find it. If it still doesn't make sense, draw the triangle out. Now, to find it--> if you know trig functions, you know you can use the function tangent, which is adj/ hyp to find the angle. since you are trying to find the angle rather than a side, you would use arc tangent instead, or tan^-1 on your calculator. You can search up on youtube more info on inverse trig functions if you'd like.
you might be asking, why use tangent and not sine or cosine? Well ,you could. But, it's better to use the information you've already been given. If you end up using sine or cosine and your answer to the first part is wrong, then your final answer will also be wrong since you calculated the wrong hypotenuse. since we've been given 40N and 60N, which is the opp and adj of our right triangle, it's best to use the tangent function just to stay safe. tangent function is tan angle = opp/adj, which is why we use that trig function. now you can use the inverse tangent function to find the angle, being angle = tan^-1(opp/adj) or arctan(opp/adj), and solve for your angle. hope this helps!!
you might be asking, why use tangent and not sine or cosine? Well ,you could. But, it's better to use the information you've already been given. If you end up using sine or cosine and your answer to the first part is wrong, then your final answer will also be wrong since you calculated the wrong hypotenuse. since we've been given 40N and 60N, which is the opp and adj of our right triangle, it's best to use the tangent function just to stay safe. tangent function is tan angle = opp/adj, which is why we use that trig function. now you can use the inverse tangent function to find the angle, being angle = tan^-1(opp/adj) or arctan(opp/adj), and solve for your angle. hope this helps!!
wait i accidentally said adj/hyp is tangent, but ITS NOT. it's opp/adj. my bad
1 answer