Answer :
Final answer:
The normal force exerted by the floor on a box pulled at a 30° angle with a force of 80 N is calculated by subtracting the vertical component of the applied force from the gravitational force. The correct normal force is 156 N.
Explanation:
The normal force exerted by the floor on a box being pulled at an angle. We are given that the box has a mass of 20 kg and is being pulled by a force of 80 N at a 30° angle above the horizontal. To find the normal force, we first need to find the vertical component of the applied force, which can reduce the normal force exerted by the floor.
We know that the normal force (N) and the gravitational force (mg) are in opposite directions. Since there is no vertical acceleration, these forces must balance each other when there is no vertical component of an applied force. The vertical component (Fv) of the applied force (80 N at a 30° angle) is calculated using the sine function: Fv = 80 N * sin(30°) = 40 N. Therefore, this vertical component reduces the gravitational force's effect on the normal force.
The gravitational force acting on the box is 20 kg * 9.8 m/s² = 196 N. Subtracting the vertical component of the applied force from the gravitational force, we get the normal force: N = mg - Fv = 196 N - 40 N = 156 N. The correct answer is (a) 156 N.
