Please help give a thorough explanation so that I can understand these problems better. Thank You!

Question

A 1300kg truck is pulling a 600kg trailer to the right by generating a 420N force. The truck is experiencing a 600N drag and the trailer experiences 340N drag. Neglect any friction impeding the motion and the mass of the cable.

How many forces are acting on the trailer?
How many forces are acting on the truck?
Are the forces on the system balanced?

What is the mass of the system?

What is the magnitude of the net force on the system?

What is the magnitude of the system's acceleration?

Describe the system's speed:

(increasing/decreasing/constant)

------>------>------->------>------>------>------>

________ ______________

| | rope | |

|_trailer__|---------------------|______truck___|

___________O____O_______________O________O________________

Answer 1

I find the question confusing in two ways:

1) "The truck ... generating a 420 N force".

Is that the force propelling the truck forward, or it is the force pulling the trailer forward?

I will assume the latter.

2) We are to neglect any friction, although trucks rely on friction for locomotion.

I will try to resolve this contradiction by postulating some unspecified force

(perhaps a giant magnet) pulling the truck forward without needing its engine.

Let

M = 1300 kg be the mass of the truck,

m = 600 kg be the mass of the trailer,

F be an unspecified force pulling the truck to the right,

f = 420 N be the tension force in the cable pulling the trailer to the right,

D = 600 N be the drag on the truck,

d = 340 N be the drag on the trailer,

a (unknown) be the acceleration of the pair (truck and trailer),

g = 9.81 m/s² be gravitational acceleration.

FORCES ACTING ON THE TRAILER:

1) downward force of gravity of magnitude mg

2) upward normal force of the road also of magnitude mg

3) rightward tension force of the cable of magnitude f

4) leftward force of drag of magnitude d

FORCES ACTING ON THE TRUCK:

1) downward force of gravity of magnitude Mg

2) upward normal force of the road also of magnitude Mg

3) some rightward force of magnitude F

4) leftward force of drag of magnitude D

5) leftward tension force of the cable of magnitude f

For both the truck and the trailer the vertical forces 1) and 2) are BALANCED.

The horizontal forces are NOT BALANCED.

MASS OF THE SYSTEM:

m + M

SYSTEM ACCELERATION:

It is easier to calculate the acceleration of the trailer alone, because we known the net force to be f-d.

By Newton's Second Law

f-d = ma

a = (f-d)/m = (420-340)/600 = 0.13 m/s²

NET FORCE ON THE SYSTEM:

By Newton's Second Law the net force on the system has magnitude

a(m+M) = (f-d)(m+M)/m = (420-340)×(600+1300)/600 = 253.3 N

The speed is increasing because there is a positive acceleration,

and the acceleration is positive because of positive net horizontal force acting on the trailer.