1.a train with a mass of 120mg accelerates uniformly on a horizontal track. The resistance to movement is 5N per kN of the mass of the train. The force in the draw bar of the locomotive is 80kN.
Calculate
A.The force required for the constant speed.
B. The force that causes the acceleration.
C. The acceleration
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.