show that v^2/r has dimensions of m/s^2

When the rate of blood flow in the aorta is 5 liter/min, the velocity of the blood in the capillaries is about 0.33 mm/sec. If the average diameter of a capillary is 0.008 mm, calculate the number of capillaries in the circulatory system.

Since neutron stars consist totally of neutrons, they are extremely massive and have a density that is hard to imagine. A typical radius and mass for a neutron star are 1.30 x 10³ m and 3.60 x 1028 kg respectively. (a) Determine the density of a neutron star. kg/m³ (b) Determine the weight (in pounds) of a penny (V = 360 mm³) if it were made from this material. (Assume 1 lb = 4.448 N.) lb

The density of copper is 9.86g. Work out the mass of the solid copper cuboid in kg Length: 10cm Width: 5 cm Height: 3 cm

Let Pa represent the density of aluminum and Pf that of iron. Find an expression of the radius (ra ) of a solid aluminum sphere that balances a solid iron sphere of radius rf on an equal-arm balance

On a part-time job, you are asked to bring a cylindrical iron rod of length 85.8 cm and diameter 2.85 cm from a storage room to a machinist. Will you need a cart? (To answer, calculate the mass of the rod. Fe = 7800 kg/m3.) Illustrate the rod with its complete dimensions based on the given information.

What is the smallest number of whole logs (ρ = 725 kg/m3, radius = 0.0840 m, length = 2.50 m) that can be used to build a raft that will carry four people, each of whom has a mass of 69.0 kg?

The mass of a bottle filled with water is found to be 150 g. The mass of the empty bottle is 50 g and the external volume of the container is 125 cm^3. Find out the density of the material of the bottle.

An automobile tire is shown in the figure below. The tire is made of rubber with a uniform density of 1.10 × 103 kg/m³. The tire can be modeled as consisting of two flat sidewalls and a tread region. Each of th sidewalls has an inner radius of 16.5 cm and an outer radius of 30.5 cm as shown, and a uniform thickness of 0.675 cm. The tread region can be approximated as having a uniform thickness of 2.50 cm (that i its inner radius is 30.5 cm and outer radius is 33.0 cm as shown) and a width of 19.4 cm. What is the moment of inertia (in kg m2) of the tire about an axis perpendicular to the page through its center? " 33.0 cm 16.5 cm Sidewall 30.5 cm Tread Enter a number. find the moment of inertia of the sidewall and the moment of inertia of the tread region. Each can be modeled as a cylinder of nonzero thickness. What is the inner and outer radius for each case? What is the formula for the moment of inertia for a thick-walled cylinder? How can you find the mass of a hollow cylinder?…

A silver sphere with a radius of 5.8 cm weighs the same as a certain aluminum cube. How long are the sides of this cube (in cm)?