A 7.5 kg box is on a table. What is the normal force acting on the box in each of the following situations?
a) You leave the box alone.
b) You push down on the box with a force if 20 N.
c) You pull up on the box with a force of 20 N.
To find the normal force acting on the box in each situation, we need to understand what the normal force is first.
The normal force is the force exerted by a surface to support the weight of an object resting on it. It is always perpendicular to the surface and acts in the opposite direction of the force applied by the object due to gravity.
a) When you leave the box alone, the only force acting on it is its weight due to gravity. The weight of an object can be calculated using the formula: weight = mass x acceleration due to gravity. In this case, the mass of the box is given as 7.5 kg. The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the weight of the box is (7.5 kg) x (9.8 m/s^2) = 73.5 N. The normal force will be equal in magnitude but in the opposite direction, so the normal force in this case is 73.5 N.
b) When you push down on the box with a force of 20 N, you are adding an additional force to the box. In this case, the normal force will not be equal to the weight of the box alone. To calculate the normal force, we need to consider the net force acting on the box, which is the sum of the weight of the box and the applied force. The net force is given by the formula: net force = mass x acceleration. Rearranging the equation, we get: net force - weight = applied force. Therefore, the normal force in this case is equal to the weight of the box minus the applied force. Normal force = weight - applied force = 73.5 N - 20 N = 53.5 N.
c) When you pull up on the box with a force of 20 N, you are again adding an additional force to the box. Similar to the previous case, the normal force will not be equal to the weight alone. Considering the net force acting on the box, we have: net force = mass x acceleration. Rearranging the equation, we get: net force + weight = applied force. Therefore, the normal force in this case is equal to the weight of the box plus the applied force. Normal force = weight + applied force = 73.5 N + 20 N = 93.5 N.