A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591 N. As the elevator later stops, the scale reading is
391 N. Assume the magnitude of the acceleration is the same during starting and stopping, and determine (a) the weight of the person, (b) the person's mass, and (c) the acceleration of the elevator
this is what i have mg+ma=591 and mg-ma=391
To solve this problem, let's break it down step by step:
(a) To find the weight of the person, we need to determine the force of gravity acting on them. We can use the formula: Weight = mass * acceleration due to gravity (g). Since weight is given by the reading on the scale, we have:
Weight + ma = 591 (Equation 1)
(b) To find the person's mass, we can use the formula: Weight = mass * g. Rearranging this equation:
mass = Weight / g (Equation 2)
(c) To find the acceleration of the elevator, we can subtract Equation 1 from Equation 2:
Weight + ma - (Weight - ma) = 591 - 391
2ma = 200
Now, let's solve the equations:
(a) Weight + ma = 591
(b) Weight + ma - (Weight - ma) = 591 - 391
(c) 2ma = 200
Simplifying equation (c):
2ma = 200
ma = 100
Now, substitute the value of ma into equation (a):
Weight + 100 = 591
Weight = 491 N
To solve equation (b), use the value of Weight in equation (a):
mass = weight / g
mass = 491 N / g
where g is the acceleration due to gravity, which is approximately 9.8 m/s².
Finally, you can calculate the person's mass and the acceleration of the elevator using the given values.