Question

an elevator is moving from up in a building. as it nears the 6th floor it slows down at a rate of 0.10m/s. a 75 kg man is standing on a scale inside the elevator. what is the scale reading?

Answer 1

To calculate the scale reading for the 75 kg man in the elevator as it slows down, we need to use the concept of weight. The weight of an object is the force exerted on it due to gravity and is given by the equation:

Weight = mass * gravitational acceleration

where the mass is given as 75 kg and the gravitational acceleration is 9.8 m/s^2.

So the weight of the 75 kg man would be:
Weight = 75 kg * 9.8 m/s^2 = 735 N

Now, when the elevator slows down, there is a force acting on the person in the opposite direction of the motion, called the apparent weight and it is given by the equation:

Apparent weight = weight - normal force

where the normal force is given by:

Normal force = m * a

where m is the mass of the object and a is the acceleration of the elevator.

As the elevator slows down, the acceleration of the elevator is the negative of the deceleration, which is -0.10 m/s^2.

So, the normal force = m * a = 75 kg * -0.10 m/s^2 = -7.5 N

Now, the apparent weight = weight - normal force = 735 N - (-7.5 N) = 735 N + 7.5 N = 742.5 N

So the scale will read 742.5 N or 742.5 kg.