The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the magnitude and direction of acceleration?
40
Netforce=ma
So the passenger is accelerating downward.
According to Newton's third law, every action has an equal and opposite reaction. Therefore, the reaction forces to the upward normal force exerted by the floor and the weight of the passenger are:
1. Reaction force to the upward normal force: The reaction force to the upward normal force is the downward normal force exerted by the passenger on the floor. Its magnitude is also 620 N, but in the opposite direction.
2. Reaction force to the weight of the passenger: The reaction force to the weight of the passenger is the gravitational force exerted by the Earth on the passenger. Its magnitude is 650 N, directed downward.
To determine if the passenger is accelerating, we need to consider the net force acting on the passenger. The net force is calculated by subtracting the downward forces from the upward forces:
Net force = upward forces - downward forces
The upward forces consist of the normal force exerted by the floor, which is 620 N, and the downward normal force exerted by the passenger on the floor, which is 620 N. Therefore, the upward forces are 620 N + 620 N = 1240 N.
The downward forces consist of the weight of the passenger, which is 650 N, and the gravitational force exerted by the Earth, which is 650 N. Therefore, the downward forces are 650 N + 650 N = 1300 N.
Now, let's calculate the net force:
Net force = upward forces - downward forces
= 1240 N - 1300 N
= -60 N
Since the net force is negative (-60 N), this means that there is a net force acting downward on the passenger. Therefore, the passenger is indeed accelerating downward.
To calculate the magnitude of acceleration, we can use Newton's second law:
Net force = mass × acceleration
Rearranging the equation, we have:
Acceleration = Net force / mass
Given that the passenger weighs 650 N, the mass can be calculated using the equation:
Weight = mass × gravitational acceleration
650 N = mass × 9.8 m/s²
mass = 650 N / 9.8 m/s²
≈ 66.33 kg
Substituting the values into the acceleration equation:
Acceleration = -60 N / 66.33 kg
≈ -0.904 m/s²
The magnitude of acceleration is approximately 0.904 m/s², and since it is negative, it indicates that the passenger is accelerating in the downward direction.
To determine the reaction forces and whether the passenger is accelerating, let's break down the problem into different forces acting on the elevator passenger.
1. Weight of the passenger: The weight of the passenger is the force exerted by gravity pulling them downward. In this case, the weight is given as 650 N.
2. Upward normal force: The upward normal force is the force exerted by the floor on the passenger. In this case, the normal force is given as 620 N.
To find the reaction forces, we need to consider Newton's third law, which states that for every action, there is an equal and opposite reaction. Therefore, the reaction forces to these two forces are:
1. Reaction to the weight of the passenger: The reaction force to the weight of the passenger is the force exerted by the passenger on the floor. It is equal in magnitude but opposite in direction to the weight, so it will be 650 N in the downward direction.
2. Reaction to the upward normal force: The reaction force to the upward normal force is the force exerted by the floor on the passenger. It is equal in magnitude but opposite in direction to the normal force, so it will be 620 N in the upward direction.
To determine if the passenger is accelerating, we need to analyze the net force acting on the passenger. Since there are two vertical forces involved, we subtract the magnitude of the upward force from the magnitude of the downward force:
Net force = Weight - Upward normal force
Net force = 650 N - 620 N
Net force = 30 N (upward)
Since the net force is positive and in the upward direction, the passenger is indeed accelerating in the upward direction.
To find the magnitude and direction of the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = mass × acceleration
In this case, we know the net force is 30 N, and we can assume the mass of the passenger remains constant. Therefore, we rearrange the equation to solve for acceleration:
acceleration = Net force / mass
acceleration = 30 N / mass (where mass should be in kg)
Without knowing the mass of the passenger, we cannot determine the exact magnitude of the acceleration. However, we know that the acceleration is positive and in the upward direction since the net force is upward.