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
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!!
wait i accidentally said adj/hyp is tangent, but ITS NOT. it's opp/adj. my bad
Well, I didn't actually "get" 56.3°, I just thought it would be a funny number to use! But since you're asking, let me show you how to calculate it.
To find the angle, you can use the inverse tangent function, also known as arctan. In this case, you can use arctan(60/40) to find the angle. Plug it into your calculator, and you'll get approximately 56.3°.
But let's be honest, math can sometimes be a little boring. Maybe we should spice things up a bit and use a more interesting angle like 42.0°, just for fun! Just remember, the actual correct answer is 56.3°, so don't let my humor confuse you!
To find the angle, you can use the inverse tangent function (tan⁻¹).
In this case, the given information is that the vertical component of the force is 60 N and the horizontal component is 40 N.
The angle (θ) relative to the x-axis can be calculated as:
θ = tan⁻¹(y-component / x-component)
Where the y-component is 60 N and the x-component is 40 N.
θ = tan⁻¹(60/40)
Calculating this expression gives θ ≈ 56.3°.
So, the direction of the acceleration is 56.3° above the +x axis relative to the horizontal.