You are working in a washing machine factory. your supervisor has asked you to design a vibration sensor for use on a washing machine when it is in its spin cycle, with the drum turning at 770 rpm. the vibration sensor consists of a cube of aluminum, with 1.50 cm edges, mounted at the top of a steel strip while the bottom of the strip is mounted to the frame of the washing machine. the strip's mass is small compared with that of the cube, but its length is large compared with the dimensions of the cube. you wish the sensor to have a resonance frequency that matches that of the washer in its spin cycle. to determine whether this will be the case, you evaluate the spring constant of the sensor by measuring the force required to pull the cube to the side by a distance of 2.65 cm while the washer is not operating. what is the magnitude of the force needed (in n) if the sensor's resonance frequency matches the spin cycle of the washer? (use 2,700 kg/m3 for the density of aluminum.) n

Note: the following questions are unrelated to the balmer series or the martian. refer to your course notes. a sun-sized star will spend most of its lifetime as a: white dwarf b. red giant c. protostar d. main-sequence star

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.)

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 kn/m and is held by cables so that it is initially compressed 50 mm. knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.