Question

2. Projectile Motion ment you will learn to describe motion in two dimensions. This lab also introduces n this experiment and provides practice wi section on uncertainty th, experimental uncertainty. In the pre-lab you are asked to read the PRE-LAB Experimental Uncertainty In a simple experiment to determine the density of steel, you select a small metal sphere that you suspect of being made of steel and measure its radius and mass. Using some simple instruments, you estimate that the sphere's radius lies in the range 1.15 cm to 1.25 cm and its mass lies in the range 60 g to 70 g. The volume of a sphere is given by V-X π r, The density (symbol p) is just the mass divided by the volume. l) Given the possible range of values for the radius, what is the range of values for the volume (i.e., find the smallest and largest possible volumes)? Show your work. Identify the values of mass and volume that lead to the smallest possible value for the calculated density. What is the density based on these values? 2) 3) Identify the values of mass and volume that lead to the largest possible value for the calculated density. What is the density based on these values? When expressing the uncertainty in a measured or calculated value, one convention is to express it in the form x ± Δ. The value x is just the midpoint between the minimum and maximum values and Ax is one half of the range of the minimum and maximum values. We Ax the absolute uncertainty. Using this notation, the radius of the ball is expressed as ( 1.20 ± 0.05) cm.
pre-lab "Projectile Motion"

Answer 1

DO NOT POST THESE MANY QUESTIONS AT ONCE.....PLEASE ABIDE BY THE RULES.

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(a) smallest possible volume = (4/3)*pi*1.15³

smallest possible volume = 6.37 cm³

largest possible volume = (4/3)*pi*1.25³

largest possible volume = 8.18 cm³

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(b)

The smallest possible value is given as

smallest density = smallest mass / largest volume

smallest density = 60 / 8.18 = 7.334 g/cm³

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(c)

The largest possible value is given as

largest density = largest mass / smallest volume

smallest density = 70 / 6.37 = 10.989 g/cm³

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(d) The mid point of range is 9.1615 and the uncertainty is 1.8275

so,

we can write is as

9.1615 +/- 1.8275