A 70kg man stands on a bathroom scale in an elevator. As the elevator starts moving, the scale reads 90kg
Is the elevator acceleration up or down, is the elevator moving up or down?
i think you mean it's weight (units in N), because mass is constant.
anyway, since the weight increased, the elevator accelerates and moves up. :)
Force up on man - weight of man = m a up
F scale - m g = m a
Fscale = 90*9.8
90*9.8 - 70*9.8 = 70 a
a = 20*9.8 /70
the acceleration is up
since we started from rest, we will be moving up but have not gained any speed yet
To determine the direction of the elevator acceleration and the direction of its motion, we need to compare the apparent weight measured by the scale to the man's actual weight.
In this scenario, the scale reads 90 kg, while the man's actual weight is 70 kg. This means that the apparent weight measured by the scale is greater than the man's actual weight.
Since the scale reading is greater than the actual weight, it suggests that the man is experiencing an upward force that is greater than his weight. This can occur in two scenarios:
1. The elevator is accelerating upward with a greater magnitude than the acceleration due to gravity (9.8 m/s^2). In this case, the scale reading is increased due to the additional upward force the man experiences during the upward acceleration.
2. The elevator is decelerating downward with a lesser magnitude than the acceleration due to gravity. In this case, the scale reading is increased due to the reduced downward force experienced by the man during the deceleration.
Based on this information, we cannot conclusively determine whether the elevator is accelerating upward or decelerating downward, or whether it is moving up or down without additional information or context.
To determine whether the elevator is moving up or down, we need to analyze the change in apparent weight on the bathroom scale.
Weight is a force caused by the Earth's gravitational pull and is equal to mass multiplied by the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the man's mass is 70 kg, so his weight is initially 70 kg * 9.8 m/s^2 = 686 N.
When the man stands on the scale in the elevator, the scale measures the normal force exerted by the man on the scale. In an elevator (or any other accelerating reference frame), there are apparent forces acting on objects due to the acceleration. These apparent forces can be lumped together as a single "net force."
If the scale reads a higher value, it means the normal force (or the apparent weight) is greater than the man's actual weight. Since the scale reads 90 kg, which corresponds to 882 N (90 kg * 9.8 m/s^2), the apparent weight is larger than the actual weight.
Now, let's consider the possible scenarios:
1. The elevator is accelerating upwards: In this case, the net force acting on the man is the sum of his weight (686 N) and the upward force exerted by the elevator. The net force is greater than the man's actual weight, resulting in a larger apparent weight on the scale.
2. The elevator is accelerating downwards: If the elevator was accelerating downwards, the net force would be the difference between the man's weight and the downward force exerted by the elevator. Since the apparent weight is greater than the actual weight, this possibility can be ruled out.
Therefore, based on the scenario you provided, it is clear that the elevator is accelerating upwards.