Frictional Forces

Question

1. A truck is hauling a trailer along a level road with a horizontal drawbar. The mass of the truck is m_truck = 9.00 x 10³ kg and the mass of the trailer is m_trailer = 1.80 x 10⁴ The two move along a straight line with an acceleration a = 1.85 m/s². If frictional forces and other retarding forces are negligible,
2. What is the magnitude of the tensional force in the horizontal drawbar?
3. What is the force from the engine of the truck that propels the truck forward?

Answer 1

#1: extract info from prompt

m_truck = 9 x 10³ kg

m_trailer = 1.8 x 10⁴ kg

a_{truck+trailer} = 1.85 m/s²

#2: just apply F=ma. The trick is to be consistent with the subscripts. In other words, use variables of the same object (e.g. truck, trailer, or both).

Tension (T) force in the drawbar?

For this part, we only consider the trailer since T only acts on the trailer. So

T = F_trailer = (m_trailer)(a_trailer)

T = (1.8 x 10⁴ kg)(1.85 m/s²) = 3.3 x 10⁴ N

Notice that I assume a_{trailer+truck} = a_trailer. This makes sense if you think of the truck and the trailer as 1 uniform object. Since this unit moves at an acceleration of 1.85 m/s², its parts are also moving at the same acceleration.

We can apply the same logic to find F_truck. Unlike F_trailer which only pulls the trailer, F_truck pulls both the truck and the trailer. So we have to take their masses into account

F_truck = (m_truck+m_trailer)(a_{truck+trailer})

= (9 x 10³kg + 1.8 x 10⁴ kg)(1.85 m/s²) = 5.0 x 10⁴ N

If you struggle to understand why we have to take m_trailer into account when we calculate F_truck, it is because we consider the truck and the trailer to be parts of 1 uniform object. We use the same line of reasoning in the first part of this prompt to say a_{truck+trailer} = a_trailer