Answer:
vi = 4.77 ft/s
Explanation:
Given:
- The radius of the surface R = 1.45 ft
- The Angle at which the the sphere leaves
- Initial velocity vi
- Final velocity vf
Find:
Determine the sphere's initial speed.
Solution:
- Newton's second law of motion in centripetal direction is given as:
m*g*cos(θ) - N = m*v^2 / R
Where, m: mass of sphere
g: Gravitational Acceleration
θ: Angle with the vertical
N: Normal contact force.
- The sphere leaves surface at θ = 34°. The Normal contact is N = 0. Then we have:
m*g*cos(θ) - 0 = m*vf^2 / R
g*cos(θ) = vf^2 / R
vf^2 = R*g*cos(θ)
vf^2 = 1.45*32.2*cos(34)
vf^2 = 38.708 ft/s
- Using conservation of energy for initial release point and point where sphere leaves cylinder:
ΔK.E = ΔP.E
0.5*m* ( vf^2 - vi^2 ) = m*g*(R - R*cos(θ))
( vf^2 - vi^2 ) = 2*g*R*( 1 - cos(θ))
vi^2 = vf^2 - 2*g*R*( 1 - cos(θ))
vi^2 = 38.708 - 2*32.2*1.45*(1-cos(34))
vi^2 = 22.744
vi = 4.77 ft/s
Answer:
The best option is for the following option m = 15 [g] and V = 5 [cm³]
Explanation:
We have that the density of a body is defined as the ratio of mass to volume.
where:
Ro = density = 3 [g/cm³]
Now we must determine the densities with each of the given values.
<u>For m = 7 [g] and V = 2.3 [cm³]</u>
![Ro=7/2.3\\Ro=3.04 [g/cm^{3} ]](https://tex.z-dn.net/?f=Ro%3D7%2F2.3%5C%5CRo%3D3.04%20%5Bg%2Fcm%5E%7B3%7D%20%5D)
<u>For m = 10 [g] and V = 7 [cm³]</u>
<u />![Ro=10/7\\Ro=1.42[g/cm^{3} ]\\](https://tex.z-dn.net/?f=Ro%3D10%2F7%5C%5CRo%3D1.42%5Bg%2Fcm%5E%7B3%7D%20%5D%5C%5C)
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<u>For m = 15 [g] and V = 5 [cm³]</u>
<u />![Ro=15/5\\Ro=3[g/cm^{3} ]\\](https://tex.z-dn.net/?f=Ro%3D15%2F5%5C%5CRo%3D3%5Bg%2Fcm%5E%7B3%7D%20%5D%5C%5C)
<u />
<u>For m = 21 [g] and V = 8 [cm³]</u>
<u />![Ro=21/8\\Ro=2.625[g/cm^{3} ]\\](https://tex.z-dn.net/?f=Ro%3D21%2F8%5C%5CRo%3D2.625%5Bg%2Fcm%5E%7B3%7D%20%5D%5C%5C)
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Answer:
In economics, elasticity is the measurement of the percentage change of one economic variable in response to a change in another.
An elastic variable (with an absolute elasticity value greater than 1) is one which responds more than proportionally to changes in other variables. In contrast, an inelastic variable (with an absolute elasticity value less than 1) is one which changes less than proportionally in response to changes in other variables. A variable can have different values of its elasticity at different starting points: for example, the quantity of a good supplied by producers might be elastic at low prices but inelastic at higher prices, so that a rise from an initially low price might bring on a more-than-proportionate increase in quantity supplied while a rise from an initially high price might bring on a less-than-proportionate rise in quantity supplied.
Elasticity can be quantified as the ratio of the percentage change in one variable to the percentage change in another variable, when the latter variable has a causal influence on the former. A more precise definition is given in terms of differential calculus. It is a tool for measuring the responsiveness of one variable to changes in another, causative variable. Elasticity has the advantage of being a unitless ratio, independent of the type of quantities being varied. Frequently used elasticities include price elasticity of demand, price elasticity of supply, income elasticity of demand, elasticity of substitution between factors of production and elasticity of intertemporal substitution.
Elasticity is one of the most important concepts in neoclassical economic theory. It is useful in understanding the incidence of indirect taxation, marginal concepts as they relate to the theory of the firm, and distribution of wealth and different types of goods as they relate to the theory of consumer choice. Elasticity is also crucially important in any discussion of welfare distribution, in particular consumer surplus, producer surplus, or government surplus.
In empirical work an elasticity is the estimated coefficient in a linear regression equation where both the dependent variable and the independent variable are in natural logs. Elasticity is a popular tool among empiricists because it is independent of units and thus simplifies data analysis.
A major study of the price elasticity of supply and the price elasticity of demand for US products was undertaken by Joshua Levy and Trevor Pollock in the late 1960s..
