Hi guys, I need a little help with this, also I need step by step thanks. 15) Yo

Question

Hi guys, I need a little help with this, also I need step by step thanks.

15) You do 168 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?
A) 22.1 kg B) 27.4 kg C) 18.8 kg D) 25.4 kg
16) An athlete stretches a spring an extra 21.5 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 52.9 N/cm?
A) 126 kJ B) 1260 J C) 126 J D) 1260 kJ
17) A tennis ball bounces on the floor three times. If each time it loses 16.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 1.9 m from the floor?
A) 130 cm B) 110 cm C) 110 mm D) 11 cm

20) A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object?
A) 0.48 m/s B) 4.3 m/s C) 7.1 m/s D) 6.6 m/s E) 3.8 m/s

Explanation / Answer

15) Work done = m g h

and h = L (1 - cos32)

168 = m x 9.8 x 5.10 (1 - cos32)

m = 22.12 kg

Ans(A)

16) U = k x^2 / 2

k = 52.9 N/cm = 5290 N/m

x = 0.215 m

U = 122.2 J

Ans(C)

17) initial energy = m g h where h = 1.9 m

a after 1st time = (1 - 0.16)mgh = 0.84 m g h

after 2nd time = 0.84 x 0.84 m g h

after 3rd time = 0.84^3 m g h

0.84^3 m g h = h'

h' = 1.1m Or 110 cm

Ans(B)

20. for elastic collision,

6.1 + 4.8 = v2 + v1

v2 = 10.9 - v1

Applying momentum conservation,

2.3 x 6.1 + (3.5 x -4.8) = - 2.3v1 + 3.5v2

-2.77 = -2.3v1 + 3.5(10.9 - v1)

-2.3v1 - 3.5v1 = -40.92

v1 = 7.1 m/s

Ans(C)

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