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A ball of mass 2 kg is thrown up with a velocity of 20 m s⁻¹. (i) Identify the sign of the work done by gravity on the ball during its upward motion and its downward motion. (ii) If the ball reaches a height of 19.4 m, how much work was done by air resistance (assume g = 10 m s⁻²).
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(i) Upward motion: gravity (down) opposes displacement (up) → negative work. Downward motion: gravity (down) is along displacement (down) → positive work.
(ii) Initial KE
=
1
2
× 2 × 20
2
= 400
J
. At the top, PE
= mgh
= 2 × 10 × 19.4
= 388
J
, KE = 0.
Energy lost to air resistance = 400 - 388 = 12 J , so the work done by air resistance = -12 J .
= v 2 2g
= 400 20
= 20 m
= mg(19.4 - 20)
= 2 × 10 × (-0.6)
= -12 J
