A group of students are trying to measure the gravitational acceierationon Earth

Question

A group of students are trying to measure the gravitational acceierationon Earth by droppngametal ball at the height of 5.0 m. Assume that each measurement carries a 10%error. They measure the time squared t2 and the distance h the ball have fallen. All the calculations should be written below. Give all numerical answers with two significant figures. h=(1/2)gh2 From the plot of h vs. t2 choose two points Pi and P2 far apart on the best fit line and find their coordinates for the slope. Pi:t2= , h= ; P2: t2 = , h = Find the slope from the graph (show your calculation) Find the gravitational acceleration g from the graph Find the % error of the measurement compared with the standard g value 9.8 m/s2 Does this experiment validate the formula you used to find the value for g?

Explanation / Answer

a:

let the two points be

( t^2 , h ) = P1 ( 0.1, 0.5) and P2 ( 0.5, 2.5 )

b:

sloap of graph = ( h(P2) - h(P1) ) / ( t^2(P2) - t^2 (P1) ) = (2.5 - 0.5) / ( 0.5-0.1 ) = 4

c:

h = ut + (1/2)*g*t^2

u = 0

h = (1/2)*g*t^2

g = 2 * (h/(t^2))

g = 2 * sloap of the curve = 2* 4 = 8 m/s^2

d:

% error in measurement of g = ( ( 9.8 - 8.0 ) / 9.8 )*100 = 18.37 % decrement

e:

definately it does validiate the formula used for the calculation of g.

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