the period of a simple pendulum, defines as the time necessary for one complete oscillation, is measured in time unites and is given by... (draw it out) where L is the length of the pendulum and G is the acceleration due to gravity , in units of length divided by time squared. show that this equation is dimensionally consistent.

A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 49 cm, height H = 15 cm, and area mass density σ.   a)   Consider a horizontal slice of the triangle that is a distance y from the top of the triangle and has a thickness dy. Write an equation for the area of this slice in terms of the distance y, and the base B and height H of the triangle.  b) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)?  c)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward.  d)Find the numeric value for the distance between the top of the triangle and the center of mass in cm.

The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L� and the acceleration of gravity is gg, then T� is given by T=2πLpgq Find the powers p� and q� required for dimensional consistency. Enter your answers numerically separated by a comma.

One mole of Gold (Au) atom has a mass of 197 g. We know that the density of gold is 19.30 g/cm3 in room temperature. Using those numbers, answer the following questions: a) What is the mass of a single gold atom in kg? b) Assume that gold atoms sit in a perfect cubic crystal structure. Estimate the distance between two gold atoms in meters.   c) If we have a gold cube of 6 cm on each side, how many atoms can we fit along the edge of each side of the cube?  d) What would be the mass, in kilograms, of the gold cube we discussed in part (c) (measuring 6 cm on each side)?

The period of a simples pendulum, defined as the time necessary for one complete oscillation l, is measured in the time units and is giving by where L is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent.

The length and width of a rectangular room are measured to be 3.885 ± 0.0065 m and 3.2 ± 0.0045 m. In this problem you can approximate the error on a product or quotient of quantities by the sum of the percent error on each quantity.Calculate the floor area of the room in square meters.

The radius of an atom of gold (Au) is about 1.35 Å. How many gold atoms would have to be lined up to span 4.0 mm? Express your answer using two significant figures.

Kinetic energy KE (Chapter 5) has dimensions kgm2/s2. It can be written in terms of the momentum p (Chapter 6) and mass m as KE = p2/2m (a) Determine the proper units for momentum (p) using dimensional analysis. (b) Refer to Problem 2. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p.

The linear density of a rod of length 4 m is given by p(x) = 8 + 2Vx measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the ra kg

Determine the absolute uncertainty for the calculated value in the following scenarios. Express as (computed result) ± (absolute uncertainty) (units).   You measure the volume of a stainless steel sphere by placing it into a100 mL graduated cylinder with an uncertainty of 1 mL, with 20 mL ofwater initially. After the sphere settles, the graduated cylinder now reads22 mL. What is the volume with uncertainty?   Please use the formula I posted ! Thank you!