eric has a mass of 60 kg. he is standing on a scale in an elevator that is accelerating downward at 1.7m/s^2. what is approximate reading on the scale?
To determine the approximate reading on the scale, we need to consider the forces acting on Eric.
1. The force due to gravity: F_gravity = m * g, where m is the mass and g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
2. The force due to acceleration: F_acceleration = m * a, where m is the mass and a is the acceleration of the elevator.
Since the elevator is accelerating downward, the net force acting on Eric is the difference between the force due to gravity and the force due to acceleration:
Net force = F_gravity - F_acceleration
Substituting the values:
Net force = (m * g) - (m * a)
Net force = (60 kg * 9.8 m/s^2) - (60 kg * 1.7 m/s^2)
Net force = (588 N) - (102 N)
Net force = 486 N
The approximate reading on the scale will be equal to the magnitude of the net force experienced by Eric, which is 486 N.
To determine the approximate reading on the scale, we need to consider the forces acting on Eric. In this case, we have Eric's weight (the force due to gravity) and the normal force exerted by the scale.
The weight of an object can be calculated using the formula:
Weight = mass * gravitational acceleration
Given that Eric's mass is 60 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate his weight:
Weight = 60 kg * 9.8 m/s^2 = 588 N
In this situation, the elevator is accelerating downward at 1.7 m/s^2. This means that there is an additional downward force acting on Eric. We can calculate this force using Newton's second law:
Force = mass * acceleration
Force = 60 kg * 1.7 m/s^2 = 102 N
Now, let's consider the forces acting on Eric. The normal force exerted by the scale is equal in magnitude but opposite in direction to the net force acting on Eric. In other words:
Normal force - Weight = Force
Since the elevator is accelerating downward, the normal force is greater than the weight. We can rearrange the equation to solve for the normal force:
Normal force = Force + Weight
Normal force = 102 N + 588 N = 690 N
Therefore, the approximate reading on the scale would be 690 N.
weight= mg-ma=m(g-a)
702kg
60(10(-1.7))= 702kg