Five children are pushing on a snowball; each pushes with a force of magnitude 10.0 N, and each is pushing at an angle of 45° relative to his neighbor. What is the magnitude of the net push on the ball?
A) 0 N
B) 24.1 N
C) 27.1 N
D) 17 N
E) 50 N

Question

Quizplus · Accepted Answer

Since each child is pushing at an angle of 45° relative to their neighbor, the forces they are applying are perpendicular to each other. Therefore, we can use the Pythagorean theorem to find the net force:

F_net = √[(F1 + F2cos(45°))^2 + (F2sin(45°) + F3cos(45°))^2 + (F3sin(45°) + F4cos(45°))^2 + (F4sin(45°) + F5cos(45°))^2 + F5sin(45°)^2]

F_net = √[(10 + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + (10sin(45°) + 10cos(45°))^2 + 10sin(45°)^2]

F_net = √[(10 + 10/√2)^2 + (10/√2 + 10/√2)^2 + (10/√2 + 10/√2)^2 + (10/√2 + 10/√2)^2 + 10/2]

F_net = √[24.1^2]

F_net = 24.1 N

Therefore, the magnitude of the net push on the ball is 24.1 N, which is closest to choice B.

Five Children Are Pushing on a Snowball; Each Pushes with a Force