to get a cart to move, to farmers pull on ropes attached to the 150 kg cart, as
ID: 2202928 • Letter: T
Question
to get a cart to move, to farmers pull on ropes attached to the 150 kg cart, as shown below. one farmer pulls with a force of 50.0 N in a direction of 35.0 degrees east of north. while the other exerts a force of 30.0 N in a direction 25.0 degrees west of north.
what are the magnitude and the direction of the combined force exerted on the cart?
considering the cart starts moving at a location labeled x=3m and y=2m, if the cart starts from rest as the farmers pull on the cart for 5minutes, calculate the magnitude and direction of the final location of the cart.
please show all work!!
Explanation / Answer
This answer is best done using components rather than trying to draw it all to scale and then measuring the length of the diagonal and measuring the angle itself. Farmer one is pulling 50 N in a direction 35 deg East of North. This means if you were to draw the compass, start at the North axis and go 35 degrees toward East. So, the North and the East components can be found using trigonometry. F1 (North) = 50 N * cos (35 deg) = 40.958 F1 (East) = 50 N * sin (35 deg) = 28.679 Similarly, F2 (North) = 35 N * cos (25 deg) = 31.721 F2 (West) = 35 N * sin (25 deg) = 14.792 So you'll add the Northern components together and subtract F2 (West) from F1 (East) since the magnitude of F1 (east) is larger. This leaves you with F1 + F2 (North) = 72.678 F1 + F2 (East/West) = 13.887 East Now, by the distance formula, the magnitude of this force = sqrt(72.678^2 + 13.887^2) = 73.993 N and the angle = atan ( 13.887 / 72.678 ) so the angle that the combined force acts on is 10.817 deg East of North
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.