An 800 N man stands on a scale in a motionless elevator. When the elevator begins to move, the scale reads 650 N. Find the magnitude and direction of the elevator's acceleration.
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To find the magnitude and direction of the elevator's acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
In this case, the man's weight or gravitational force is acting downwards with a magnitude of 800 N.
When the elevator begins to move, there is an additional force acting on the man. This force is the normal force exerted by the scale and is equal to the difference between the man's weight and the reading on the scale. In this case, the scale reading is 650 N. Therefore, the normal force is 800 N - 650 N = 150 N acting upwards.
To find the acceleration, we need to calculate the net force acting on the man. The net force is the vector sum of the gravitational force and the normal force.
Since we know the net force and the mass of the man is not given, we cannot directly calculate the acceleration. However, we can determine the direction of the acceleration.
Since the normal force is less than the gravitational force, the net force will have a downward component. Therefore, the direction of the elevator's acceleration is downwards.