if I weigh 177 lb on a stationary scale and stand on that same scale inside an elevator going up at an acceleration of 12 ft/s^2 the scale will read 238lbs. if the elevator, still moving upwards, decelerates at the rate of 32 ft/s^2 what will the scale read?
177 (12+32)/32 = 243 I get
but anyway
177 (32 -32) = 0
To determine what the scale will read when the elevator decelerates at a rate of 32 ft/s^2, we need to consider the changes in the apparent weight caused by the acceleration and deceleration.
Let's break down the problem step by step:
Step 1: Calculate the apparent weight when the elevator accelerates upward at 12 ft/s^2.
When the elevator goes upward with an acceleration of 12 ft/s^2, the apparent weight will increase. To find the apparent weight, we need to add the force due to acceleration to the normal weight.
Normal weight = 177 lb
Force due to acceleration = mass × acceleration
To convert from weight (lb) to mass (lbm), divide the normal weight by the acceleration due to gravity (32.2 ft/s^2).
mass = 177 lb / 32.2 ft/s^2 = 5.49 lbm
Force due to acceleration = 5.49 lbm × 12 ft/s^2 = 65.88 lb
Apparent weight = Normal weight + Force due to acceleration
Apparent weight = 177 lb + 65.88 lb = 242.88 lb (approximately 243 lb)
Step 2: Calculate the apparent weight when the elevator decelerates at 32 ft/s^2.
When the elevator decelerates at 32 ft/s^2 while still moving upward, the apparent weight will decrease. To find the apparent weight, we need to subtract the force due to deceleration from the previous apparent weight.
Force due to deceleration = mass × deceleration
Using the same mass as before (5.49 lbm) and a deceleration of 32 ft/s^2:
Force due to deceleration = 5.49 lbm × 32 ft/s^2 = 175.68 lb
Apparent weight = Previous apparent weight - Force due to deceleration
Apparent weight = 242.88 lb - 175.68 lb = 67.20 lb
Therefore, when the elevator decelerates at 32 ft/s^2, the scale will read approximately 67.20 lb.