It's part of "Homework Questions for New Higher Physics" but there are no answers at the back of the book and I can't find them anywhere online, so I can't even look ahead and try to figure it out by working backwards.
It's from the chapter "Newton 2".
The vehicle on the air track is pulled by a falling mass of 0.2kg. The mass of the air track vehicle is 1.1kg.
a) show, by calculation, that the air track vehicle and the falling mass both accelerate at 1.51ms-2.
I know that they accelerate together, since they're attached, so they'll have the same acceleration. They're on an air track, so I don't need to think about friction. I'm so lost, I have no idea what to do here, which makes me feel like I'm probably over-looking something simple, but it's been a couple of days now that I've been going back to it and I just can't work out what to do. *sigh*
I hope someone can help me out!
1) for the falling particle
2) for the vehicle?
Then you need to rearrange F = ma to give the acceleration with the combined mass of the car and falling mass with the force calculated above. (a = f/m). This is because the pulling string couples the mass of both objects, meaning that the force acts on them as if they are one.
Of course we are assuming the string is light and inextensible. To be pedantic, the solution formally requires us to state that the force acting on the car is T, and T = m(car) x a. Then, state the force acting on the falling mass as an equation: (m(mass) x g) - T = m(mass) x a. Then you can substitute T out by using the previous equation for the car, arriving in the same place as my solution above.
Note that even when using tension rather than intuition, if you require the acceleration what you do is consider the mass of both and the force experienced by the falling object by substituting tension out.
I actually don't know how I hadn't been able to see how to do the second part. I think once I'd got confused I just couldn't see past that to the right answer, even though it makes complete sense now.