Math Snap

STEP 1

What is this asking?
How strong is the pull between the tractor and the first cart if the whole train is moving at a steady speed?
Watch out!
Don't get tricked by all the numbers!
Constant velocity means zero acceleration.

STEP 2

1. Visualize the forces
2. Calculate the total mass being pulled
3. Find the force

STEP 3

Imagine the train moving at a constant speed.
That means the tractor is pulling just hard enough to keep everything moving at $4.5$ m/s.
No speeding up, no slowing down!

STEP 4

The tractor (T) is pulling all the carts ($M_1$, $M_2$, and $M_3$).
The force between T and $M_1$ is what's keeping those carts moving.

STEP 5

The tractor is pulling $M_1$, $M_2$, and $M_3$.
Let's add those masses together to find the total mass being pulled by the tractor.

STEP 6

$$\text{Total Mass} = M_1 + M_2 + M_3$$ $$\text{Total Mass} = 40 \text{ kg} + 15 \text{ kg} + 10 \text{ kg}$$ $$\text{Total Mass} = \mathbf{65} \text{ kg}$$So, the tractor is pulling a total of 65 kg of carts!

STEP 7

Since the train is moving at a constant velocity, the net force is zero!
This means the force the tractor exerts is perfectly balanced by other forces (in this case, there are no other forces since we're told there's no friction).
Newton's second law tells us: $F = ma$.

STEP 8

Since the velocity is constant, the acceleration ($a$) is zero.
$$F = m \cdot a$$ $$F = 65 \text{ kg} \cdot 0 \frac{\text{m}}{\text{s}^2}$$$$F = \mathbf{0} \text{ N}$$

STEP 9

The net force acting on the entire train is zero, but we're looking for the force between the tractor (T) and the first cart ($M_1$).
This force is what's pulling the carts $M_1$, $M_2$, and $M_3$.

STEP 10

Since the net force on the three carts is also zero, the force between the tractor and $M_1$ must be zero.

The force in the connection between the tractor (T) and cart $M_1$ is $\mathbf{0} \text{ N}$.