A student of mass 80kg stands on a spring scale in an elevator.During the first 3seconds,starting from rest,the scale reads 80kg.Determine the velocity of the elevator at the end of the 3seconds,and the tension T in the supporting cable during the acceleration period.The total mass of the elevator,student and scale is 805kg.
if the scale reads a static weight of 80gk, the scale is not accelerating. So at the end of three seconds, the scale is at some constant velocity, it has not moved since the force never changed.
Tension=805*g
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To determine the velocity of the elevator at the end of the 3 seconds, we can use the equation of motion:
v = u + at
Where:
v = final velocity of the elevator
u = initial velocity of the elevator (which is 0 m/s since it starts from rest)
a = acceleration of the elevator
t = time (which is 3 seconds)
We need to find the acceleration of the elevator. The only force acting on the elevator is the tension T in the supporting cable. According to Newton's second law, the force on an object is equal to its mass times its acceleration:
F = ma
The force experienced by the elevator is the difference between its weight (mg) and the tension in the cable (T):
F = mg - T
Since the scale reads the weight of the student (80 kg) during the acceleration period, we can substitute the mass of the elevator (805 kg) and the acceleration (a) into the equation:
805a = (805 kg)(9.8 m/s^2) - T
Simplifying the equation:
805a = 7899 kg m/s^2 - T
Now, we can solve for T:
T = 7899 kg m/s^2 - 805a
Next, we substitute the values into the equation v = u + at:
v = (0 m/s) + (a)(3 s)
v = 3a
Now, we can equate the values of T and v:
7899 kg m/s^2 - 805a = 3a
To solve for a, we rearrange the equation:
808a = 7899 kg m/s^2
a = 7899 kg m/s^2 / 808
a ≈ 9.775 m/s^2
Now that we have the acceleration (a), we can calculate the tension (T):
T = 7899 kg m/s^2 - 805(9.775 m/s^2)
T ≈ 1004.4 kg m/s^2
Therefore, the velocity of the elevator at the end of the 3 seconds is approximately 29.326 m/s, and the tension in the supporting cable during the acceleration period is approximately 1004.4 kg m/s^2.