Astudent wish to measure the gravitational acceleration g. she does it by releasing a small lead ball from rest and measures the time t it takes the ball to drop a distance s. g can then be found using the relation t2. she measures t using an automated digital timer which manual states that it measures drop times up to 500 ms with an uncertainty of 3 ms. she sets the system up such that s 100.0 t 0.3 mm (measured using a measurement tape), and the timer reads that the drop time is 144 1 ms. calculate her best estimate of g and its uncertainty . discuss how she could set up her experiment such that she would achieve a better precision in a single drop, without needing a more precise timer or being able to measure distances with higher precision

(9.64 +- 0.86) m/s^2

Explanation:

The generic motion equation for constant acceleration is

Where

X0: initial position

v0: initial speed

a: acceleration

t: time

If the object has an initial speed of zero, and the frame of reference is set conveniently so that the object initial position is zero, the equation simplifies to:

And the acceleration can be obtained as:

Where x is the distance fallen and a = g.

So, with the data x = (100.0 +- 0.03) mm and t = (144 +- 3) ms we can calculate

For the uncertainty we have to calculate the relative uncertainties first

For the distance (100 * 0.3)/100 = 0.3%

For the time (100 * 3)/144 = 2.08%

For multiplications or divisions the relative uncertainties are added

0.3% + 2.08% + 2.08% = 4.46%

We convert this into absolute uncertainty:

(9.64e-3 * 4.46)/100 = 0.00043 mm/(ms^2)

Finally, this is multiplied by a constant scalar, so:

2 * 0.00043 mm/(ms^2) = 0.00086 mm/(ms^2)

We convert the units

0.86 m/(s^2)

And the measurement is (9.64 +- 0.86) m/s^2

A better method is putting the ball in a ramp instead of a free fall, that way the fall is longer and the effect of time measuring uncertainty is reduced.

igneous rocks also form where plates converge. the subducting plate melts as it sinks into the crust of the earth, and the melt rises into the overriding plate forming volcanoes. metamorphic rocks are formed mainly in the lithosphere, wherever there is high pressure and high temperature. -woods