Question

Corey, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 820 N for the first 3.0 s after the elevator starts to move, then 930 N for the next 3.0 s.

Part A:
What is the elevator's velocity 6.0 s after starting? Express your answer with the appropriate units. Enter a positive value if the motion is upward and a negative value if the motion is downward.

Answer 1

The elevator's velocity 6.0 seconds after starting is 6.96 m/s, indicating an upward motion.

Step-by-step explanation:

To determine the elevator's velocity 6.0 seconds after starting, we can calculate the change in reading on the bathroom scale during the first 6.0 seconds. From the given information, the scale reads 820 N for the first 3.0 s and 930 N for the next 3.0 s. The change in reading is 930 N - 820 N = 110 N. Since force is directly proportional to mass and acceleration, we can use Newton's second law (F = ma) to find the acceleration of the elevator. Rearranging the equation, we have a = F/m. Using the mass of Corey (95 kg) and the change in reading (110 N), we find that the acceleration is a = 110 N / 95 kg = 1.16 m/s^2. With the acceleration and the time (6.0 s), we can use the equation v = u + at to find the velocity. Plugging in the values, we have v = 0 m/s + (1.16 m/s^2)(6.0 s) = 6.96 m/s. Since Corey is initially at rest, a positive velocity of 6.96 m/s means the motion is upward.