To calculate the force required for constant speed, the resistive force needs to be determined. The resistive force is given as 5N per kN of the mass of the train.
Given:
Mass of the train (m) = 120 mg = 120 × 10⁻³ kg
Resistive force per kN of mass (R) = 5 N/kN
A. Force required for constant speed (F₁):
The resistive force can be calculated by multiplying the resistive force per kN of mass with the mass of the train:
Resistive force (Fr) = R × mass of the train
= (5 N/kN) × (120 × 10⁻³ kg)
= 0.6 N
Therefore, the force required for constant speed (F₁) is 0.6 N.
To calculate the force that causes acceleration, we need to subtract the resistive force from the force in the drawbar of the locomotive.
Given:
Force in the drawbar (F) = 80 kN
B. Force that causes acceleration (F₂):
To find the force that causes acceleration, subtract the resistive force from the force in the drawbar of the locomotive:
Force that causes acceleration (F₂) = Force in the drawbar - Resistive force
= (80 kN) - (0.6 N)
= 79.4 kN
Therefore, the force that causes acceleration (F₂) is 79.4 kN.
C. Acceleration (a):
To calculate acceleration, we need to use Newton's second law of motion, which states that the force applied is equal to the mass of the object multiplied by its acceleration.
Given:
Mass of the train (m) = 120 mg = 120 × 10⁻³ kg
Force that causes acceleration (F₂) = 79.4 kN = 79.4 × 10³ N
Rearranging the formula:
Force that causes acceleration (F₂) = mass of the train (m) × acceleration (a)
Solving for acceleration (a):
Acceleration (a) = Force that causes acceleration (F₂) / mass of the train (m)
= (79.4 × 10³ N) / (120 × 10⁻³ kg)
= 662,666.67 m/s²
Therefore, the acceleration (a) is 662,666.67 m/s².