Florence who weighs 120lb stands on a bathroom scale in an elevator. What will she see the scale read when the elevator is accelerating upward at 4.0 m/s^2
a) 120lb
b) 135lb
3) 105lb
d) 90lb
Well, Florence might see her weight fluctuating more than during her usual elevator rides. But let's analyze the situation with a hint of humor!
Considering that the elevator is accelerating upwards, Florence will actually feel heavier, like she just ate an entire pizza by herself! So, the scale will show a value greater than her normal weight. Therefore, the correct answer is b) 135lb. Time to lay off the pizzas, Florence!
To determine what Florence will see on the scale, we need to consider the forces acting on her in the elevator.
When the elevator is accelerating upward at 4.0 m/s^2, Florence experiences two forces:
1. Gravitational Force (Weight):
The gravitational force is due to Florence's mass and acts downward. This force is equal to Florence's weight, which is 120lb.
2. Acceleration Force:
The acceleration force is due to the elevator's upward acceleration and acts in the same direction as the elevator's motion. This force can be calculated using Newton's second law: F = m * a, where F is the force, m is the mass, and a is the acceleration.
Since Florence's mass remains constant, the acceleration force will be F = m * a = 120lb * 4.0 m/s^2.
To find out what Florence sees on the scale, we need to calculate the net force acting on her. The net force is the difference between the acceleration force and gravitational force.
Net Force = Acceleration Force - Gravitational Force
= (120lb * 4.0 m/s^2) - 120lb
To determine the scale reading, we need to convert the net force into weight (force). 1lb = 4.448 N (approximately).
Net Force (in N) = Net Force (in lb) * 4.448 N/lb
Now let's calculate the scale reading:
Net Force (in N) = (120lb * 4.0 m/s^2 - 120lb) * 4.448 N/lb
After calculating this expression, we will have the net force in Newtons (N). Then we can convert it back into pounds (lb) to determine the scale reading.
Please note that without the actual numerical value for "120lb," we cannot determine the specific scale reading.
To determine what Florence will see on the bathroom scale when the elevator is accelerating upward at 4.0 m/s^2, we need to consider the effect of the acceleration on her weight.
When an object is in an elevator accelerating in a particular direction, it experiences a pseudo-force in the opposite direction of the acceleration. This pseudo-force is often referred to as the "apparent weight" or "effective weight". It is the force exerted by a scale on the object due to the contact between them.
To find the apparent weight on the scale, we can use the following equation:
Apparent weight = Actual weight + Pseudo-force
In this case, the actual weight of Florence is 120 lb. The pseudo-force acting on her is given by:
Pseudo-force = mass × acceleration
We can convert Florence's weight from pounds to kilograms since the acceleration is given in meters per second squared. 1 lb is approximately equal to 0.454 kg. Therefore, Florence's mass is:
mass = weight / gravitational acceleration
mass = 120 lb × 0.454 kg/lb ≈ 54.48 kg
Now, we can calculate the pseudo-force:
Pseudo-force = mass × acceleration
Pseudo-force = 54.48 kg × 4.0 m/s^2 ≈ 217.92 N
Finally, we can find the apparent weight on the scale:
Apparent weight = Actual weight + Pseudo-force
Apparent weight = 120 lb + 217.92 N
Since we need to provide the answer in pounds, we can convert the apparent weight from Newtons to pounds by using the gravitational acceleration conversion factor:
1 N ≈ 0.2248 lb
Apparent weight in pounds ≈ (120 lb + 217.92 N) × (0.2248 lb/N)
Calculating the above expression, we get:
Apparent weight in pounds ≈ 120 lb + 48.98 lb ≈ 169.98 lb
Therefore, Florence would see the scale read approximately 170 lb. Hence, the answer is not listed among the options given.