Math Group
Question:
jharry23
Student
College - Junior
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.)
Answers:
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kjcdb8er Teacher
eNotes Editor
Posted by kjcdb8er on Tuesday September 22, 2009 at 8:49 AMThe 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).
↘ ↓
→ O
↗ ↑
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.
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neela Teacher
Graduate SchooleNotes Editor
Posted by neela on Tuesday September 22, 2009 at 9:44 AMLet 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.
