Swing Seat
Betty weighs 424 N and she is sitting on a playground swing seat that hangs 0.29 m above the ground.?
Betty weighs 424 N and she is sitting on
a playground swing seat that hangs 0.29 m
above the ground. Tom pulls the swing back
and releases it when the seat is 1.2 m above
the ground.
The acceleration of gravity is 9.8 m/s2 .
1. How fast is Betty moving when the swing
passes through its lowest position?
Answer in units of m/s.
010 (part 2 of 2) 10.0 points
2. If Betty moves through the lowest point at
1.4 m/s, what is the magnitude of the work
done on the swing by friction?
Answer in units of J.
1) Tom does work equal to the force (Betty’s weight) times the distance lifted. This work is stored as gravitational potential energy. When Betty moves through the lowest position, that gravitational potential energy (in the absence of losses due to air resistance, friction, etc.) is converted to kinetic energy:
mgh = ½mv²
2gh = v²
√(2gh) = v
Putting in the numbers,
v = √[2(9.8)(1.2 - 0.29)] ≈ 4.223 m/s (I’ll let you decide how many digits to use)
2) If Betty moves through the lowest point at only 1.4 m/s, then her kinetic energy (in joules) is ½(424/9.8)(1.4)² ≈ 84.8 J. The kinetic energy she would have had in the absence of friction is, from question 1, mgh = (424)(0.91) ≈ 385.8 J. The difference is due to the work done on the swing by friction. The magnitude of this work, then, is (385.8 – 84.8) = 301 J.
GTA 4 Swing Glitch Location
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