A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate: (a) the net accelerating force and (b) the acceleration of the train.

Question

An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s^–1 to 8 m s^–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer 1

Given:

Mass of engine, \( m_e = 8000 \, \text{kg} \)
Mass of each wagon, \( m_w = 2000 \, \text{kg} \), number of wagons = 5
Force exerted by engine, \( F_{\text{engine}} = 40000 \, \text{N} \)
Friction force, \( F_{\text{friction}} = 5000 \, \text{N} \)

Step 1: Total mass of train

\[ m_{\text{total}} = m_e + 5 \cdot m_w = 8000 + 5 \cdot 2000 = 18000 \, \text{kg} \]

Step 2: Net accelerating force

\[ F_{\text{net}} = F_{\text{engine}} - F_{\text{friction}} \] \[ F_{\text{net}} = 40000 - 5000 = 35000 \, \text{N} \]

Step 3: Acceleration of the train

Using Newton's second law: \[ a = \frac{F_{\text{net}}}{m_{\text{total}}} = \frac{35000}{18000} \approx 1.94 \, \text{m/s²} \]

Answer:

(a) Net accelerating force = 35000 N
(b) Acceleration of the train = 1.94 m/s²