0.7 Ball bearing with measured radius that is correct to within 0.01 inch.
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The measured radius of a ball bearing is 0.7 inch, Ball bearing with measured radius that is correct to within 0.01 inch. 0.7 as shown in the figure. The measurement is correct to within 0.01 inch. Estimate the propagated error in the volume V of the ball bearing.
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- In the diagram below there is a thick-walled cylindrical tube. Its height is H = 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2 = 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p x h?. R2 a) Proof that the proportionality constant k (p = kh?) is k = , ms 100m b) Determine the position of the center of mass of this object. c) Determine I, the moment of inertia of the cylindrical tube around the axle going through the center of the top (as shown on diagram). You can use lying =mr? (the rotational inertia of a ring of radius r and mass m rotating around an axis parallel to it, through its center).Calculate the mass (in SI units) of a 140 lblb human being. Express your answer with the appropriate units.What is the approximate mass of air in a living room 4.3 m x 3.4 m x 2.8 m? The density of air is 1.29 kg/m³. Express your answer to two significant figures and include the appropriate units. HẢ ? Value Units т
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- helpA Tire has a radius of 0.34 m. If it is driven of 2.7 km, What is the total angle that it has rotated ?Consider a water tank that is being filled with rainfall at the top and is drained through a small hole atthe bottom. The change in volume can be modelled by considering the amount of water entering andleaving the tank (per unit of time) as followsdVdt= fin − fout.Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout isin litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.(a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t andthat the tank is losing 10% of its volume of water per hour, such that, fout(V ) = 0.1V . Check bydirect substitution that the functionV (t) = 10(t + 5e−0.1t)satisfies the ODE and the initial condition.Now assume that the hole is slowly growing in size, so that the flow rate out increaseswith time:fout(V, t) = 0.1(1 + 0.1t)V.Solve the ordinary differential equation for V (t) with this flow rate out, using either separation…