a 75kg person is standing on a scale in an elevator, the scale gives a readout in newtons(you have to use a free body diagram)determine the reading on the scale in newtons in each of the following situations, when the elevator is not moving, the elevator is moving upward at 2 m/s, the elevator is moving downward at 2 m/s, the elevator is accelerating upward at 2 m/s^2,the elevator is accelerating downward at 2 m/s^2, if the reading on the scale is 840 newtons determine the elevator's acceleration
assume g=9.8m/s^2, and acceleration is + upwards.
Weight=m(g+a)
notice constant motion(ie speed) is not a factor in the equation.
To determine the reading on the scale in each situation, let's analyze the forces acting on the person using a free body diagram.
When the elevator is not moving:
In this case, the person is standing still relative to the elevator, so there is no vertical acceleration. The only force acting on the person is gravity, which can be calculated using the formula F = m * g, where m is the mass (75 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, the reading on the scale would be equal to the weight of the person, which is:
Weight = mass * gravity = 75 kg * 9.8 m/s^2 = 735 N
Therefore, the reading on the scale when the elevator is not moving would be 735 N.
When the elevator is moving upward at 2 m/s:
In this situation, the person experiences an upward acceleration due to the elevator's motion. The forces acting on the person are gravity and the normal force from the scale. The normal force cancels out a part of the gravitational force to provide an upward net force. Since the person is in equilibrium (not accelerating) relative to the elevator, the net force must be equal to zero.
Net force = Upward normal force - Downward gravitational force
Let's denote the reading on the scale as R.
R - m * g = 0
R = m * g
R = 75 kg * 9.8 m/s^2
R = 735 N
So, the reading on the scale when the elevator is moving upward at 2 m/s would also be 735 N. The acceleration of the elevator does not affect the scale reading in this case.
Similarly, when the elevator is moving downward at 2 m/s, the reading on the scale would still be 735 N because the person is experiencing the same forces as before, just in the opposite direction.
Now, let's consider the cases when the elevator is accelerating.
When the elevator is accelerating upward at 2 m/s^2:
In this scenario, the person experiences an additional upward force due to the elevator's acceleration. The net force on the person is the sum of the normal force, gravitational force, and the force due to acceleration.
Net force = Upward normal force - Downward gravitational force + Upward force due to acceleration
Let's denote the reading on the scale as R and the acceleration of the elevator as a.
R - m * g + m * a = 0
Since we are given that the reading on the scale is 840 N, we can solve for the acceleration.
840 N - (75 kg * 9.8 m/s^2) + (75 kg * a) = 0
Simplifying the equation:
840 N - 735 N + 75 kg * a = 0
75 kg * a = (840 N - 735 N)
75 kg * a = 105 N
a = (105 N) / (75 kg)
a = 1.4 m/s^2
Therefore, the elevator's acceleration when the reading on the scale is 840 N would be 1.4 m/s^2.
Similarly, we can follow the same approach to determine the elevator's acceleration when it is accelerating downward at 2 m/s^2.