Three dynamics carts have force sensors placed on top of them.(cart 1, with mass of 2.2 kg, has one sensor --> cart 2, with mass of 2.5 kg, has sensors two and then three --> cart 3, with mass of 1.8 kg, has sensors four then five). Each force sensor is tied to a string that connects all three carts together. You use a sixth force sensor to pull the three dynamics carts forward. (cart 1 being at the back, cart three at the front, right behind the sixth sensor). The reading on force sensor 2 is 3.3 N. Assume that the force sensors are light and that there is negligible friction acting on the carts.

Question

What is the acceleration of all the carts?

The answer is apparently 1.5 m/s/s, but I don't know how to get it! I know acceleration = force/mass, but the force of 3.3N is only on the second sensor so I don't think that would apply for all of the carts. I'm stuck; please help!

Answer 1

If you just do a FBD on the last cart and ignore all the rest a = F/m = 3.3/2.2 = 1.5
A classic example of useless smoke and mirrors.

Answer 2

The force is the same for all the carts so add them up. Then, add up all the mass.

Net force=massxacceleration
9.9N=6.5xacceleration
1.5m/s^2=acceleration

Answer 3

i dont know the answer this is why i am here to learn the method from this website thank you.

Answer 4

The acceleration is the same all around as all the carts are connected. Therefore it would be impossible for a cart to have a different acceleration than the others.

Fnet= ma
rearranged to:
a= Fnet/m
= 3.3/2.2
= 1.5 m/s^2