# What is the magnitude of the total force on the ball?5 boys are pushing on a snowball, and each is pushing with a force of 10.0N. however, each boy is pushing in a different direction. they are...

What is the magnitude of the total force on the ball?

5 boys are pushing on a snowball, and each is pushing with a force of 10.0N. however, each boy is pushing in a different direction. they are pushing north, northeast, east, southeast, and south. (Each boy is pushing at an angle of 45.0 degrees relative to his neighbor.)

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### 2 Answers

The total force on the ball is the sum of every individual force vector pushing on the ball.(note that we're excluding gravity, which would point down into the screen).

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Note that in the y direction, all the forces will cancel. So the net force vector will be pointing in the x direction. We have 10 N + 2*10N*cos45 = 10N(1 + 2*sqrt(2)/2) = 24.14 N in the x direction.

The magnitude then, is 24.14, since the force in the y direction is zero.

Let A ,B C ,D and E be the persons who push the ball north , north east, east, south east and sothern directions. Resolving the force of each in North and eastern directions , we get:

A; 10 cos 0 = 10N towards north and 10 sin0 =0N east

B:10 cos 45=10/sqrt2Nnorth and 10 sin 45 =10/sqrt2N east

C: 10 cos90 =0N north and 10 sin90 = 10N east

D: 10 cos (-135)= -10/sqrt2 N and 10 sin135 = 10/sqrt2

E: 10 cos 180 = -10 N north and 10 sin 180 =0 east

Therefore: thesum of north components=(10+10/srt2+0-10/sqrt2-10)= 0 and the total of east components =2(10/sqrt2)+10 = 10(2/sqrt2 +10=10(sqrt2+1) N = 24.1421N approximately. Therefore the resultant of 0 north and 24.1421 N towards east is 24.1421 N and in eastern direction.