Five boys are pushing on a snowball,and each is pushing with a force of 10.0 N.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 $\degree$relative to his neighbor. )What is the magnitude of the total force on the ball?
A)0
B)17.1 N
C)24.1 N
D)27.1 N

Question

Quizplus · Accepted Answer

Since the forces are all at 45 degrees to each other, we can use vector addition to find the total force.

First, we can find the horizontal and vertical components of each force using trigonometry. Since they are all the same magnitude, each force has a component of 10.0 N cos(45°) = 7.07 N in the horizontal direction, and a component of 10.0 N sin(45°) = 7.07 N in the vertical direction.

Next, we can add up all the horizontal components and all the vertical components separately to get the total horizontal and vertical components of the force.

Total horizontal force = (7.07 N + 7.07 N + 10.0 N + 7.07 N - 7.07 N) = 24.1 N to the right
Total vertical force = (7.07 N + 10.0 N + 7.07 N - 7.07 N - 7.07 N) = 10.0 N up

Finally, we can use the Pythagorean theorem to find the magnitude of the total force:

Total force = sqrt((24.1 N)^2 + (10.0 N)^2) = 27.1 N

So the answer is (C) 24.1 N.

Five Boys Are Pushing on a Snowball,and Each Is Pushing °\degree°

Five Boys Are Pushing on a Snowball,and Each Is Pushing $\degree$