A woman stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.70 of her regular weight.
1).Calculate the magnitude of the acceleration of the elevator.
Express your answer to two significant figures and include the appropriate units.
2).Find the direction of the acceleration.
To calculate the magnitude of the acceleration of the elevator, we can use the equation:
Weight on the scale = mass * acceleration due to gravity
The woman's regular weight is equal to her mass multiplied by the acceleration due to gravity. Let's call the woman's regular weight W. We can calculate her regular weight using the equation:
W = m * g
where m is her mass and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
When the elevator accelerates upwards, the scale reads only 0.70 of her regular weight. Let's call this reduced weight W'.
W' = 0.70 * W
Now, let's express the reduced weight in terms of mass and acceleration due to gravity:
W' = m * g'
where g' is the effective acceleration due to gravity when the elevator is in motion.
Equating these two expressions for W', we have:
m * g' = 0.70 * m * g
Since the mass cancels out on both sides of the equation, we have:
g' = 0.70 * g
Now we can substitute the value of g (approximately 9.8 m/s^2) into the equation to find g':
g' = 0.70 * 9.8 m/s^2
g' = 6.86 m/s^2
Therefore, the magnitude of the acceleration of the elevator is approximately 6.86 m/s^2.
To find the direction of the acceleration, we need to consider the reduced weight measured by the scale. Since the scale reads only 0.70 of her regular weight, it means that the net force acting on the woman is less than the force due to gravity. This reduction in weight suggests that the elevator is accelerating downwards while the woman is standing on it. Therefore, the direction of the acceleration of the elevator is downwards.