Five boys are pushing on a snowball,and each is pushing with a force of 16.0 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° relative to his neighbor. )What is the magnitude of the total force on the ball?
A) 0
B) 23 N
C) 38.6 N
D) 17.4 N
E) 77.3 N

Question

Five boys are pushing on a snowball,and each is pushing with a force of 16.0 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° relative to his neighbor. )What is the magnitude of the total force on the ball?​
A) 0
B) 23 N
C) 38.6 N
D) 17.4 N
E) ​77.3 N

Quizplus · Accepted Answer

To solve this problem, we need to use vector addition. We can start by drawing a diagram with arrows representing the magnitude and direction of each boy's force. Each arrow will be 16.0 N long and at a 45-degree angle to its neighbors. Then, we can use the parallelogram rule to find the resultant force.

The resultant force is the diagonal of the parallelogram formed by the four forces. The magnitude of this diagonal can be found using the Pythagorean theorem, since the forces are all at 45-degree angles.

The length of one side of the parallelogram is 16.0 N, and the length of the other side is 32.0 N (since there are two forces at a 45-degree angle on each side). Using the Pythagorean theorem, we find that the magnitude of the resultant force is:

F = sqrt((16.0 N)^2 + (32.0 N)^2) = 38.6 N

Therefore, the magnitude of the total force on the ball is 38.6 N. The correct answer is (C).

Five Boys Are Pushing on a Snowball,and Each Is Pushing