The average value for h1 is ¼(h11+ h12 + h13 + h14) = 1/4 ( 9.8 cm + 10.0 cm + 9

Question

The average value for h1 is

¼(h11+ h12 + h13 + h14) = 1/4 ( 9.8 cm + 10.0 cm + 9.9 cm + 9.8 cm ) = 9.875 cm

The height for h is equal to

h1 – h0 =   9.875 cm - 7.0 cm = 2.875 cm

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The average value for X:

= 1/4 ( X1 + X2 + X3 + X4 )

= 1/4 ( 204 cm + 220 cm + 221 cm + 219 cm )

= 216 cm

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Find velocity of pendulm:

vp = [ ( 2 g ) ( h1 – h0 ) ] 1/2

vp = [ ( 2 ) ( 9.8 ) ( 0.02875 m ) ] 1/2

vp = 0.75 m/s

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Velocity of ball:

vb = [ ( mb +mp ) / mb ) ] vp

= [ ( 0.368 kg + 0.065 kg )/ 0.065 kg ] (  0.75 m/s )

= 5.00 m/s

Percentage of Difference = ?

Percentage of Error= [(Velocity1-Velocity2)/Average V1+V2]x100%=?

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Explanation / Answer

Here,

The average of group of no is given as,
Avg = (x1 + x2 + x3 + ......xn) / n   

Where n is total no of instances, while x1,x2 etc are value of instances.

Part 1:
The average value for h1 is
¼(h11+ h12 + h13 + h14) = 1/4 ( 9.8 cm + 10.0 cm + 9.9 cm + 9.8 cm ) = 9.875 cm
The height for h is equal to
h1 – h0 = 9.875 cm - 7.0 cm = 2.875 cm

Part 4:
The average value for X:
= 1/4 ( X1 + X2 + X3 + X4 )
= 1/4 ( 204 cm + 220 cm + 221 cm + 219 cm )
= 216 cm

Part 3 :
From Third Eqn of motion,
v^2 - u^2 = 2*a*hn ( hn = change in height while swinging)

rewriting for velocity of pendulum
v = sqrt(2*g*(h1-h0))

Part 4
This exmple is of Conservation of momenntum, where object move together after collision,

initial momentum before collision = momentum after collision

mb*vb + mp*vp = Vp(mb+mp)

Velocity of ball:
vb = ( ( mb + mp ) / mb ) vp
= [ ( 0.368 kg + 0.065 kg )/ 0.065 kg ] ( 0.75 m/s )
= 5.00 m/s

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