Question

A 45 kg person in an elevator on a platform scale FRQ.

a) Determine the force exerted by the person on the scale
b) Calculate the acceleration of the elevator
c) Evaluate the gravitational potential energy
d) Measure the lift force acting on the person

Answer 1

The force exerted by the person on the scale is equal to their weight, which is the product of mass and gravitational acceleration, approximately 441 N (Newtons).Option A is correct.

Step-by-step explanation:

In this scenario, the person's weight is the force they exert on the scale. Weight is calculated by multiplying mass (45 kg) by the gravitational acceleration (approximately 9.8 m/s²). Therefore, the force exerted by the person on the scale is 45 kg * 9.8 m/s² = 441 N.

b) To calculate the acceleration of the elevator, we need additional information such as the direction of motion (upward, downward, or at rest) and the net force acting on the person-elevator system. Newton's second law (F = ma) can be applied to find the acceleration.

c) Gravitational potential energy depends on the height of the person above a reference point. If this information is provided, the potential energy can be calculated using the formula PE = mgh, where m is mass, g is gravitational acceleration, and h is the height.

d) The lift force acting on the person is essentially the force exerted by the elevator on the person, which can be calculated by considering the net force acting on the person-elevator system.

Option A is correct.

Answer 2

The scale reading is calculated using Newton's second law, resulting in a force of 1860 N, which is much greater than the woman's normal weight of 735 N due to the elevator's high acceleration rate of 15.0 m/s².

Step-by-step explanation:

Calculating Elevator Scale Reading

When a 75.0-kg woman stands on a scale in an accelerating elevator, we can calculate the scale reading using Newton's second law. The elevator accelerates from rest to 30.0 m/s in 2.00 s. The apparent weight is the normal force exerted by the scale (Fs), which is equal to the actual weight (mg) plus the force due to the elevator's acceleration (ma). Hence:

Fs = m(g + a)

The acceleration a of the elevator is given by:

a = ∆v/∆t = 30.0 m/s / 2.00 s = 15.0 m/s²

We calculate Fs as:

Fs = (75.0 kg) * (9.80 m/s² + 15.0 m/s²) = (75.0 kg) * (24.8 m/s²) = 1860 N

Therefore, the scale shows a force of 1860 N, which is the reading that will be compared to her normal weight. Her normal weight (w) would be calculated using:

w = mg = (75.0 kg) * (9.80 m/s²) = 735 N

Comparing 1860 N to 735 N, the scale reading is significantly higher when the elevator is accelerating.

Identifying Unreasonable Aspects

A scale reading indicating 1860 N is unreasonable because it is much greater than her actual weight and suggests a very high acceleration, which would be uncomfortable or potentially dangerous for passengers. The unreasonable premise might be the high acceleration rate within such a brief time period.