6. At the end of a graduation ceremony, the graduates 1.18m.--. fing their caps

Question

6. At the end of a graduation ceremony, the graduates 1.18m.--. fing their caps into the air. Suppose a 0.120 kg cap is thrown straight upward with a speed of 7.85 m/s and that frictional forces can be ignored. v,-7.85 m/s a. Find the speed of the cap when it has risen 1.18 m above the fling point. b. Find the maximum height of the cap. c. In real life (because of friction) the cap comes back to its original height (y-0 in the image) with a speed of 6.90 m/s. How much heat was released to the environment? For each item, draw energy way diagrams showing initial and final states.

Explanation / Answer

a)

m = mass of the cap = 0.120 kg

vi = initial speed of the cap = 7.85 m/s

vf = final speed of the cap at height of 1.18 m = ?

h = height = 1.18 m

Using conservation of energy

initial kinetic energy = final kinetic energy + potential energy

(0.5) m vi2 = (0.5) m vf2 + mgh

vi2 = vf2 + 2gh

(7.85)2 = vf2 + (2 x 9.8 x 1.18)

vf = 6.2 m/s

b)

H = maximum height

at maximum height , the final kinetic energy becomes 0

hence

Using conservation of energy

initial kinetic energy = final kinetic energy + potential energy

(0.5) m vi2 = mgH

H = (0.5) vi2 /g

inserting the values

H = (0.5) (7.85)2 /9.8

H = 3.14 m

c)

vi = initial speed of launch = 7.85 m/s

vf = final speed when cap returns = 6.90 m/s

work done by frictional force is given as heat

heat = change in kinetic energy

heat = (0.5) m(vi2 - vf2)

inserting the values

heat = (0.5) (0.120)((7.85)2 - (6.90)2)

heat = 0.84 J

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