The average car today has a mass of 1100 kg, and when accelerating from rest, covers 0.25 miles in 15 seconds. Each rim and tire together has a diameter of 46 cm and a mass of 9.1kg. If we agree the rim and tire have the shape of a solid disk that rotates through its geometric center, what would be the kinetic energy of one of the tires, in Joules, at the end of the run?
I know KE=Iw^2
I calculated the moment of inertia to be 1.0465 kg*m
to find w, i calculated the number of revolutions for the given distance to be 278. dividing by time = 18.5rev/sec
converting to rad 116 rad/sec
so Ke= 116^2*1.0465 = 14081.704 j
am i right? i also need help with sig figs
Yes, you are on the right track with your calculations. Let's break it down step by step to ensure accuracy.
First, you correctly identified the formula for kinetic energy: KE = I * w^2, where KE is kinetic energy, I is moment of inertia, and w is angular velocity.
To find the moment of inertia (I), you need to know the mass of the tire (m) and its radius (r). The mass of the tire is given as 9.1 kg, but we need to find the radius. The diameter of the tire is given as 46 cm, which means the radius is half of that, or 23 cm (or 0.23 m).
Now, we need to convert the mass of the tire from kg to kg*m^2. This conversion is done by multiplying the mass by the square of the radius: I = m * r^2 = 9.1 kg * (0.23 m)^2 = 1.0463 kg*m^2 (your value was slightly rounded, so this is the more accurate one).
Next, we need to find the angular velocity (w). You correctly calculated the number of revolutions per second to be 18.5 rev/sec. To convert this to radians per second, multiply by 2π since there are 2π radians in one revolution: w = 18.5 rev/sec * 2π rad/rev = 116.136 rad/sec (your value was rounded to 116 rad/sec, which is close enough for this calculation).
Lastly, we can compute the kinetic energy by plugging in the values into the formula: KE = I * w^2 = 1.0463 kg*m^2 * (116.136 rad/sec)^2 ≈ 14081.3 J (rounded to five significant figures).
As for significant figures, the general rule is to maintain the same number of significant figures as the least precise measurement. In this case, 0.25 miles and 15 seconds both have two significant figures, so the final answer should be rounded to two significant figures as well. Therefore, the correct answer would be 14000 J (or 1.4 × 10^4 J).
Make sure to use appropriate rounding and sig fig rules in future calculations to ensure accuracy.