A train consists of two carts and an engine. If m = 1000 kg, and the train is moving with an acceleration of 5.5 m/s2, find the tensions between the engine and the middle cart.
T1 is the tension in the coupling between the locomotive and the first car,
T2 the tension in the coupling between the first and the second car.
Newton’s 2 law for the first car is
ma = T1-T2, .......(1)
for the second car:
ma =T2,............(2)
Plug (2) in (1)
ma = T1 – ma,
T1 = 2 ma = 2•1000•5.5 =11000 N
To find the tension between the engine and the middle cart, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the middle cart has a mass of m = 1000 kg and is moving with an acceleration of 5.5 m/s². Therefore, we can calculate the force acting on the middle cart using the formula:
Force = mass × acceleration
Force = 1000 kg × 5.5 m/s²
Force = 5500 N
Since the force acting on the middle cart is equal to the tension between the engine and the middle cart, the tension between them is 5500 N.