Assume that a scale is in an elevator on the earth. What force would the scale exert on a 53 kg person standing on it when the elevator slows at 1.77 m/s2 while moving upward?
To determine the force exerted by the scale on the person, we need to consider two forces: the gravitational force and the net force acting on the person in the elevator.
First, let's calculate the gravitational force acting on the person. The gravitational force can be calculated using the equation:
F_gravity = m * g
where m is the mass of the person (53 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
F_gravity = 53 kg * 9.8 m/s^2
F_gravity ≈ 519.4 N
The gravitational force acting on the person is approximately 519.4 Newtons.
Next, we need to consider the net force acting on the person in the elevator. The net force is determined by the equation:
Net force = mass * acceleration
In this case, the acceleration is the acceleration of the elevator, which is given as -1.77 m/s^2. The negative sign indicates that the elevator is slowing down while moving upward.
Net force = 53 kg * (-1.77 m/s^2)
Net force ≈ -93.81 N
The net force acting on the person in the elevator is approximately -93.81 Newtons.
Finally, the force exerted by the scale on the person can be found by subtracting the net force from the gravitational force:
Force exerted by the scale = F_gravity - Net force
Force exerted by the scale = 519.4 N - (-93.81 N)
Force exerted by the scale ≈ 613.21 N
Therefore, the scale would exert a force of approximately 613.21 Newtons on the 53 kg person standing on it when the elevator slows at 1.77 m/s^2 while moving upward.