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Problem 73 Medium Difficulty

ssm 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.

Answer

18.0 $\mathrm{m} / \mathrm{s}^{2}$
$56.3^{\circ}$

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Video Transcript

to find the magnitude of acceleration, we have to find the magnitude off the net force that acts on that object. So in this on the subject there to forces acting, these one and these one. So the vector sum off this forces is the following. So we have a 60 Newton force and then we have a 40 new don't force. So these will be in that force. These high party news here, then this is a rectangle triangle. These side of the triangle has 60 these other sites has 40 and here we have did not force. Then, by using the Pythagorean theorem, we got the net force off, square it off 40 squared plus 60 squared, which results in approximately 72 Newton's. Then we can use Newton's second law to determine what is the acceleration. Because Newton's second law tells us that the magnitude of the net force is equal to the mass of the object size and magnitude off the objects acceleration. Then the acceleration is equals to the net force divided by the mass. The net force is approximately 72 new terms and the mass is for kilograms. So this gives us an acceleration off 18 meters per second squared. Now we have to defer minus direction with respect to the X axis. So let me draw the net force here in the object. So the net force will be pointing in the yard, you know, like this. And it makes an angle with the X axis or the horizontal axes which in the direction that bundle I will call Teeter. So here we have Tita. Then we have to note in mind what is Dita So using the same rectangle triangle that we had user before we conduct her mind once the value off Tita Because here, Tito using this site. So here we have teeter. It's the angle in between the hypotheses on the 14 YouTube side. Then we can calculate, for instance, the sign or the co sign or the tangent off. Peter, I'll go with the tangent. So the tangent off detail is given by the opposite side, divided by the address inside. And these results in six divided by four or three divided by truth or 1.5 then Tita is the inverse tangent off 1.5, which is approximately 56 0.3 degrees. Then the direction is 56.3 degrees above the X axis

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