A roller coaster with passengers has a mass of 400 kg. At the top, the coaster is assumed to be at rest. Determine the minimum height, h, that it must start from in order to go around a 40 m diameter loop without falling off the track at the top of the loop. Take h to be the distance from the ground and the bottom of the loop is also at the ground level.

Acommon technique in analysis of scientific data is normalization. the purpose of normalizing data is to eliminate irrelevant constants that can obscure the salient features of the data. the goal of this experiment is to test the hypothesis that the flux of light decreases as the square of the distance from the source. in this case, the absolute value of the voltage measured by the photometer is irrelevant; only the relative value conveys useful information. suppose that in part 2.2.2 of the experiment, students obtain a signal value of 162 mv at a distance of 4 cm and a value of 86 mv at a distance of 5.7 cm. normalize the students' data to the value obtained at 4 cm. (divide the signal value by 162.) then calculate the theoretically expected (normalized) value at 5.7 cm.