A 24.5 kg child sits on a bathroom scale which is placed on the seat of...

A 24.5 kg child sits on a bathroom scale which is placed on the seat of a swing. What does the scale read when the swing is at rest? The child begins to swing back and forth until she reaches a maximum height of 0.85 meters (measured vertically) above the low point. What will the scale read as she passes the low point? The swing rope is 3.0 meters long.

Solutions

Expert Solution

a) 24.5 kg, or 9.8x24.5 = 240 newtons depending on the scale. They all read in kg, but classroom problems are in newtons.

b) you need to calculate the speed, and you can do that via energy exchange.

Kinetic Energy in J if m is in kg and V is in m/s
KE = ½mV²
Potential Energy in J
PE = mgh
g is the acceleration of gravity 9.8 m/s²
½mV² = mgh
V = √(2gh) = √(2•9.8•0.85) = 4.08 m/s

now use the circular motion math to get the centrifugal force.
Centripetal force f = mV²/r = mrω²
F = (24.5)(16.66) / 3 = 136 newtons

At the low point, this adds to her weight or
F = 240 + 136 = 376 newtons
Converting to kg, that is 38.4 kg

genius_generous answered 1 year ago

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