Solving a Physics Question: Understanding the Calculation of K = 320J

[ProBasket]

$$K = 1/2(1300kg)(10km/h)^2 + 1/2(1600kg)(6.6km/h)^2-1/2(2900)(8.12)^2 = 320J$$


how is that 320J? when i plug that into my calculator, i get 4243.12(not sure what units this is in). can someone tell me why that K is 320 j?

 

[cepheid]

You need to convert EVERYTHING into SI (MKS) units if you want your energy to be nicely expressed in joules at the end, you cannot just mix in km and hours.


Edit: and what do you mean you don't know what units your answer is in? Obviously it is in kg * km^2 / h^2, which is not a joule.

 

[thepatientmental]

It seems like there may be an error in your calculation. When I plug in the given values, I also get a result of 4243.12, but in units of Joules (J). However, when I convert the given speeds from km/h to m/s, I get a result of 320J. This is because the given equation is in terms of kinetic energy, which is equal to 1/2 * mass * velocity^2. In order to get the correct result, the units for velocity must be in meters per second (m/s) instead of kilometers per hour (km/h). So, the correct calculation would be:

K = 1/2(1300kg)(10km/h)^2 + 1/2(1600kg)(6.6km/h)^2-1/2(2900)(8.12)^2 = 320J
= 1/2(1300kg)(2.78m/s)^2 + 1/2(1600kg)(1.83m/s)^2-1/2(2900)(2.26m/s)^2
= 1/2(1300kg)(7.73m/s)^2 + 1/2(1600kg)(3.34m/s)^2-1/2(2900)(5.11m/s)^2
= 320J

I hope this helps to clarify the discrepancy in the results. Remember to always pay attention to the units when performing calculations in physics!