1. Florence, who weighs 560 N,
1. Florence, who weighs 560 N, stands on a bathroom scale in anelevator. What will she see the scale read when the elevator isaccelerating upward at 5 m/s2?(g = 9.8 m/s2) Newtons
2.You swing a 3.41 kg bucket of water in a vertical circle ofradius 0.900 m. At the top of the circle the speed of the bucket is3.25 m/s. Find the tension in the rope tied to the bucket at thetop of the circle
Answer:
Scale already reads (560/ 9.8) = 57.14 kg when elevatoris at rest.
Now, force on the man in the upward direction from acceleratingup (force E) = mass of the man x acc. of the lift in the upwarddirection = 57.14 x5 N = 285.7 N.
Now force of gravity (Fg) = 560 N.
Plus the normal force (n) -which keeps him fallingthrough floor of elevator – is also acting on him = 686 N (same asgravity in up direction).
So, F(y) = Elevator (Up) 285.7 (up) + Normal (up) 560 N -Gravity (down) 560 N.
Therefore net force in the upward direction (againstbottom of scale-floor) = (+385 + 686 – 686) N = 285.7N.
Hence the reading of the scale has extra = (285.7N).Scale is calibrated for “g = 9.8 m/ss”.
So, (285.7 / 9.8m/ss) kg = 29.15 kg extra. So, 29.15 kg(extra) + 57.14kg (original) = 86.3 kg. This is why you feelheavier when elevator goes up.
2)
T = m * v^2/ R – m * gT = m (v^2 / R – g)
T = 3.41 * {(3.25^2 / 0.9) – 9.8}
T= 6.6 N
so the tension in the rope at the top of the circle is6.6 N
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