A pendulum consists of a massless stiff rod of length L hanging from a nearly frictionless axle, with a mass m at the end of the rod. Calculate the gravitational potential energy as a function of the angle, θ, measured from the vertical. Set U = 0 at the location of the mass when the pendulum is hanging straight down.

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

1. how much energy is needed to raise the temperature of 40.0 g of argon from 25c to 40c? the specific heat capacity of argon is 0.520 j/(g·k) 2a. 23.0 ml of 0.100 m hcl (standard) are added from a buret to neutralize 50.0 ml of an unknown basic solution. 2b. if the oh- produced in the previous reaction came from ca(oh)2, then what is the molarity of the ca(oh)2? 3.calculate the new freezing-point of a solution when 60.5 grams of cacl2 solute is dissolved in 0.612 kg of water. 4. what is the maximum number of moles of alcl3 that can be produced from 5.0 mol al and 6.0 mol cl2? 5. a sample of oxygen gas has a volume of 150 ml when its pressure is 0.923 atm. if the pressure is increased to 0.987 atm and the temperature remains constant, what will the new volume be? 6. nitrogen gas in a closed container at a temperature of 100.0 oc and 3.0 atm is heated to 300 oc. what is the pressure of the gas at the higher temperature?

Select the three ways that the parallel-plate capacitor differs from a car battery.