A 490 newton woman stands on a bathroom scale while riding in a elevator that is accelerating downward at 2m/sec/sec. Find her apparent weight and her apparent mass. Compare to her starting mass.
To find the woman's apparent weight, we need to consider the forces acting on her. When the elevator is accelerating downward, we have two forces: her actual weight (mg) acting downward, and the normal force (N) exerted by the scale acting upward. The net force is the difference between these two forces, which causes her apparent weight.
The equation we can use is:
Net Force = Apparent Weight - Actual Weight
Newton's second law states that:
Net Force = mass x acceleration
Where:
- Net Force is the difference between the normal force and the actual weight.
- Apparent Weight is the weight she feels on the scale.
- Actual Weight is her real weight (mg).
- Mass is her mass.
- Acceleration is the acceleration of the elevator.
Let's solve for her apparent weight and apparent mass:
Step 1: Calculate the actual weight:
Actual Weight = mass x gravity
Given that the woman's actual weight is 490 N, we can rearrange the equation to solve for her mass:
490 N = mass x (9.8 m/s²)
Step 2: Calculate the net force:
Net Force = mass x acceleration
The acceleration of the elevator is given as 2 m/s².
Step 3: Calculate the apparent weight:
Apparent Weight = Actual Weight - Net Force
Now, let's plug the values into the equation:
Apparent Weight = 490 N - (mass x 2 m/s²)
Step 4: Compare the apparent mass to the starting mass:
Apparent Mass = Apparent Weight / gravity
Starting Mass = Actual Weight / gravity
To compare the apparent mass and starting mass, we divide the apparent weight and actual weight by the acceleration due to gravity (9.8 m/s²).
Now that we have calculated all the variables, we can find the answers to the given question. However, we need the value for the acceleration of gravity to proceed. Please provide the value for the acceleration due to gravity, or we can use the standard value of 9.8 m/s² if you prefer.