Kirsten’s mass is 3.73 slugs. Being the physics fan that she is, she decides to see what her apparent weight will be during an elevator ride. Beginning at rest, the elevator accelerates upward at 4.50 ft/s2 for 3.00 s and then continues at a constant upward velocity. Finally, as the elevator comes to a stop at the top floor, the elevator slows down (accelerates downward but continues to move upward) at a rate of 5.5 ft/s2 (the negative sign represents the downward direction). Find Kirsten’s weight while the elevator is (a) at rest. (b) speeding up. (c) moving at a constant velocity. (d) slowing down. The next time you ride in an elevator, concentrate on when you feel heavier and when you feel lighter.
g = 32.2 ft/s
(a) 3.73 * 32.2 = w (lbs)
(b) 3.73 * (32.2 + 5.5) = w
(c) same as (a)
(d) 3.73 * (32.2 - 5.5) = w
(a) While the elevator is at rest, Kirsten's weight will be the same as her actual weight. So, she will feel the crushing weight of all her responsibilities and the heaviness of the world on her shoulders. Just kidding! She'll feel the same weight as usual.
(b) When the elevator is speeding up, Kirsten will feel lighter. Sort of like that feeling when you let go of your responsibilities for a moment and just go with the flow. Wheee!
(c) When the elevator is moving at a constant velocity, Kirsten's weight will remain the same as her actual weight. It's like the constant in a math equation. Unchanging, predictable, and slightly boring. But hey, at least she won't feel any heavier!
(d) When the elevator is slowing down, Kirsten will feel heavier than her actual weight. Just like the weight of unmet deadlines or the sinking feeling of realizing you forgot to turn off the stove before leaving the house. Gravity seems to play tricks on us when we least expect it!
To find Kirsten's weight in different scenarios during the elevator ride, we need to consider the forces acting on her.
(a) When the elevator is at rest:
In this case, the elevator is not accelerating, and Kirsten's weight will be equal to her actual weight. The gravitational force acting on her can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that her mass is 3.73 slugs, and the acceleration due to gravity is approximately 32.2 ft/s², we can calculate her weight:
Weight = 3.73 slugs * 32.2 ft/s² = 120.0 lb
So, Kirsten's weight while the elevator is at rest is 120.0 lb.
(b) When the elevator is speeding up:
During this phase, the elevator is accelerating upward at a rate of 4.50 ft/s². Kirsten will feel heavier due to the additional force exerted on her. The net force acting on her can be calculated using Newton's second law:
Net force = mass * acceleration
The net force includes the force of gravity and the upward acceleration of the elevator. The formula becomes:
Net force = mass * (acceleration due to gravity + elevator acceleration)
Net force = 3.73 slugs * (32.2 ft/s² + 4.50 ft/s²)
Net force = 3.73 slugs * 36.7 ft/s²
Net force ≈ 136.85 lb
So, Kirsten's weight while the elevator is speeding up is approximately 136.85 lb.
(c) When the elevator is moving at a constant velocity:
When the elevator is moving at a constant velocity, it means there is no acceleration. In this case, the net force acting on Kirsten is zero since the gravitational force is balanced by the upward force exerted by the elevator. So, her weight remains the same as in (a), which is 120.0 lb.
(d) When the elevator is slowing down:
During the slowing down phase, the elevator is accelerating downward at a rate of -5.5 ft/s². Kirsten will feel lighter due to the reduced net force acting on her. Using the same formula as in (b), the net force becomes:
Net force = 3.73 slugs * (32.2 ft/s² - 5.5 ft/s²)
Net force = 3.73 slugs * 26.7 ft/s²
Net force ≈ 99.75 lb
So, Kirsten's weight while the elevator is slowing down is approximately 99.75 lb.
Remember, the feeling of "heaviness" or "lightness" experienced during an elevator ride is due to the net force acting on our bodies. When the net force is greater than the force of gravity, we feel heavier, and when the net force is smaller than the force of gravity, we feel lighter.
To find Kirsten's weight in different scenarios, we need to consider the forces acting on her. The weight of an object is the force due to gravity acting on it. In this case, we will consider Kirsten's apparent weight, which is the force she perceives while in the elevator.
(a) When the elevator is at rest:
At rest, the elevator does not accelerate, so there is no force acting on Kirsten other than her weight. The apparent weight is equal to her actual weight. Therefore, Kirsten's weight in this case is 3.73 slugs.
(b) When the elevator is speeding up:
During this phase, the elevator is accelerating upward at 4.50 ft/s^2. To find Kirsten's apparent weight, we need to consider the net force acting on her. The net force is the sum of the gravitational force (weight) and the force due to the acceleration of the elevator.
The net force is given by the equation:
Net Force = Mass * Acceleration
Since Kirsten's mass is given as 3.73 slugs, we can calculate the net force:
Net Force = 3.73 slugs * 4.50 ft/s^2
Once we have the net force, we can find Kirsten's apparent weight by dividing the net force by the acceleration due to gravity (32.2 ft/s^2):
Apparent Weight = Net Force / Acceleration due to gravity
Therefore, Kirsten's weight while the elevator is speeding up is:
Apparent Weight = (3.73 slugs * 4.50 ft/s^2) / 32.2 ft/s^2
(c) When the elevator is moving at a constant velocity:
When the elevator is moving at a constant velocity, there is no acceleration and thus no net force acting on Kirsten. The only force acting on her is her weight. Therefore, her apparent weight is equal to her actual weight, which is 3.73 slugs.
(d) When the elevator is slowing down:
In this situation, the elevator is accelerating downward at a rate of -5.5 ft/s^2. We need to calculate the net force and then find Kirsten's apparent weight using the same process as in part (b).
First, calculate the net force:
Net Force = Mass * Acceleration
Net Force = 3.73 slugs * (-5.5 ft/s^2)
Then, find Kirsten's apparent weight:
Apparent Weight = Net Force / Acceleration due to gravity
So, Kirsten's weight while the elevator is slowing down is:
Apparent Weight = (3.73 slugs * -5.5 ft/s^2) / 32.2 ft/s^2
During a normal elevator ride, you may feel heavier when the elevator is accelerating upward and lighter when it's accelerating downward, as these accelerations affect your apparent weight.