an elevator and its load have a total mass of 1000 kg. find the tension in the supporting cable if the elevator originally moving downward at 10m/s is brought to rest with a constant acceleration after moving a distance of 50m?
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To find the tension in the supporting cable, we need to analyze the forces acting on the elevator.
There are two forces acting on the elevator:
1. The force due to gravity, which is equal to the weight of the elevator and its load.
2. The tension force in the supporting cable.
First, let's determine the weight of the elevator and its load. The weight is the mass multiplied by the acceleration due to gravity (g). Assuming g is approximately 9.8 m/s²:
Weight = mass * g
Weight = 1000 kg * 9.8 m/s²
Weight = 9800 N
Since the elevator is initially moving downward at 10 m/s and is brought to rest, there is an acceleration acting in the upward direction. Let's call this acceleration "a".
We can use the kinematic equation to relate the variables, s (distance), u (initial velocity), v (final velocity), a (acceleration), and t (time):
v² = u² + 2as
In this case, the final velocity v is 0 m/s (since the elevator comes to rest), the initial velocity u is -10 m/s (negative sign indicates downward direction), and the distance s is 50 m.
0² = (-10)² + 2a(50)
0 = 100 - 100a
100a = 100
a = 1 m/s²
Now we can find the tension force in the supporting cable using Newton's second law (F = ma):
Tension - Weight = mass * acceleration
Tension - 9800 N = 1000 kg * 1 m/s²
Tension - 9800 N = 1000 N
Tension = 1000 N + 9800 N
Tension = 10800 N
Therefore, the tension in the supporting cable is 10800 Newtons.