Question

1. A gust of wind blows an apple from a tree. As the apple falls, the force of gravity on the apple is 9.34 N downward, and the force of the wind on the apple is 1.34 N to the right. What is the magnitude of the net external force on the apple? Answer in units of N.

2. What is the direction of the net external force on the apple (measured from the downward vertical, so that the angle to the right of downward is positive)? Answer in units of ◦.

Answer 1

1. 9.43 N

2. 8.27◦

Step-by-step explanation:

1. To find the magnitude of the net external force on the apple, we need to add the forces of gravity and the wind together. The force of gravity on the apple is 9.34 N downward, and the force of the wind on the apple is 1.34 N to the right. We can use the Pythagorean theorem to find the magnitude of the net external force:

F = sqrt(Fg^2 + Fw^2) = sqrt(9.34^2 + 1.34^2) = sqrt(87.1936 + 1.7956) = sqrt(89.0592) = 9.43 N

Therefore, the magnitude of the net external force on the apple is approximately 9.43 N.

2. To find the direction of the net external force on the apple, we need to use the forces of gravity and the wind to form a right triangle. The force of gravity on the apple is the hypotenuse of the triangle, and the force of the wind on the apple is one of the legs. We can use the inverse tangent function (arctan) to find the angle between the force of gravity and the force of the wind:

θ = arctan(Fw/Fg) = arctan(1.34/9.34) = arctan(0.1427) = 8.27◦

The angle of 8.27◦ is measured from the downward vertical, so the net external force on the apple is in the direction 8.27◦ to the right of downward.