train with 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 locomotive is 80kN
Calculate
a. The force required for constant speed
b. The force that causes the acceleration
c. The acceleration
I'm having trouble visualizing a train with a mass of 120 mg. Even toy trains are heavier than that.
Okay please assist me with the calculations
To solve this problem, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. We also need to consider the resistance force acting against the motion of the train.
a. The force required for constant speed:
For the train to maintain a constant speed, the net force acting on it must be zero. The force of resistance is given as 5N per kN of mass. Since the mass of the train is given as 120mg (milligrams), we need to convert it to kilograms:
Mass of the train = 120mg = 120 * 10^(-6) kg = 0.00012 kg
To find the force required for constant speed, we need to balance the weight of the train with the resistance force:
Force required for constant speed = Weight of the train + Force of resistance
Weight of the train = mass * gravitational acceleration
Gravitational acceleration = 9.8 m/s^2
Weight of the train = 0.00012 kg * 9.8 m/s^2 = 0.001176 N
Force of resistance = (Force of resistance per unit mass) * mass
Force of resistance per unit mass = 5 N/kN * 0.00012 kg = 0.0006 N
Force required for constant speed = 0.001176 N + 0.0006 N = 0.001776 N
Therefore, the force required for constant speed is 0.001776 N.
b. The force that causes the acceleration:
The force that causes the acceleration is the difference between the force in the draw-bar locomotive and the resistance force. The force in the draw-bar locomotive is given as 80 kN, which needs to be converted to N:
Force in the draw-bar locomotive = 80 kN * 1000 N/kN = 80000 N
Force that causes the acceleration = Force in the draw-bar locomotive - Force of resistance
Force that causes the acceleration = 80000 N - 0.0006 N = 79999.9994 N
Therefore, the force that causes the acceleration is approximately 79999.9994 N.
c. The acceleration:
Using Newton's second law of motion, we can find the acceleration of the train.
Net force = mass * acceleration
79999.9994 N = 0.00012 kg * acceleration
Solving for acceleration:
acceleration = 79999.9994 N / 0.00012 kg
Therefore, the acceleration of the train is approximately 666,666.661 m/s^2.
To calculate the force required for constant speed, we need to consider the resistance to movement and the force applied by the locomotive.
a. The force required for constant speed is equal to the resistance to movement. The resistance to movement is given as 5N per kN of the mass of the train. Since the mass of the train is 120mg, which is equivalent to 0.12kg, we can calculate the resistance:
Resistance = (5 N/kN) * (0.12 kg) = 0.6 N
Therefore, the force required for constant speed is 0.6 N.
b. The force that causes acceleration is the difference between the force applied by the locomotive and the resistance.
Force causing acceleration = Force applied by the locomotive - Resistance
= 80kN - 0.6N
= 79.4 kN
Therefore, the force that causes the acceleration is 79.4 kN.
c. To calculate the acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Acceleration = Force causing acceleration / mass
= (79.4 kN) / (0.12 kg)
= 661.7 m/s^2
Therefore, the acceleration of the train is 661.7 m/s^2.