# Test tomorrow... trouble with conversion.

by ital_dj
Tags: conversion, solved, test, trouble
 P: 31 Hi, I'm in Grade 11 Physics, and I have a Unit 1 Test tomorrow on motion and forces. I'm not the smartest, so I can't exactly tell if the book is wrong. I'm doing a question out of the book, and was wondering what answers you guys come up with. The question is: Calculate the net force acting on a 20kg object if the acceleration is: a) 9.8m/s$$^{2}$$ b) 0.28m/s$$^{2}$$ c) 5669km/h$$^{2}$$ d) (50km/h)/s Currently, I'm stuck on c). The book says the answer is 8.8N, and I'm getting 3160N. The calculated a value I got was 158m/s$$^{2}$$. If I'm wrong, can you tell me how to correct myself? Thanks a lot for your help, guys.
 P: 568 Reason you have to use the conversion factor twice is because units must obey the same laws of algebra that numbers do. See "dimensional analysis" in the index of your textbook. If you did: km m h ---- ---- ---- h^2 km s then the units will fail to cancel out to give exactly m/s^2 and nothing else. But if you do: km m h h ---- ---- ---- ---- h^2 km s s then the units cancel and all you are left with is m/s^2.
 P: 568 I'll tell you where most people make this particular type of mistake: in conversions related to area and volume. For example, suppose a certain liquid has a density of 1 g/cm^3. Let's convert that density to the SI unit of kg/m^3. To make the units cancel out properly, I'm going to have to use the conversion factor (100 cm / 1m) three times!  g 1 kg 100 cm 100 cm 100 cm 1 ------ ------- -------- -------- -------- cm^3 1000 g 1 m 1 m 1 m kg = 1000 ---- m^3