a train with a mass of 120Mg accelerates uniformly on a horizontal track. The resistance to movement is 5N per kN mass of the train. The force in the draw bar is 30kN. Calculate:
a) The force required for a constant speed
b) The force that cause acceleration
c)The acceleration
To solve this problem, we'll break down the different forces acting on the train and use Newton's second law of motion (F = ma) to calculate the required values.
Given data:
Mass of the train (m) = 120 Mg (1 Mg = 1000 kg)
Resistance per mass (R) = 5 N/kN
Force in the draw bar (F) = 30 kN
a) The force required for constant speed:
For constant speed, the force of acceleration is zero. Therefore, the force required for constant speed is equal to the resistance force.
Force required for constant speed (Fc) = Resistance force
Given that the resistance is 5 N per kN mass of the train, we can calculate the resistance force (Rf):
Rf = (R * m) = (5 N/kN * 120 Mg) = (5 N/kN * 120,000 kg) = 600,000 N
Therefore, the force required for constant speed (Fc) is 600,000 N.
b) The force that causes acceleration:
To calculate the force that causes acceleration, we need to subtract the resistance force from the force in the draw bar.
Force causing acceleration (Fa) = Force in the draw bar - Resistance force
Fa = (F - Rf) = (30 kN - 600,000 N) = 29,400,000 N
Therefore, the force that causes acceleration (Fa) is 29,400,000 N.
c) The acceleration:
To calculate the acceleration, we can use Newton's second law of motion (F = ma). Rearranging the formula, we have:
a = F / m
Given that the force causing acceleration (Fa) is 29,400,000 N and the mass of the train (m) is 120 Mg (120,000 kg), we can calculate the acceleration (a):
a = (Fa / m) = (29,400,000 N / 120,000 kg) = 245 m/s^2
Therefore, the acceleration (a) is 245 m/s^2.
To solve this problem, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. We can use the equation:
F = ma
where F is the net force, m is the mass, and a is the acceleration.
a) The force required for a constant speed:
When the train is moving at a constant speed, the net force acting on the train is zero (since there is no acceleration). The force of resistance to movement is given as 5N per kN mass of the train. So, the force of resistance to movement can be calculated as:
Force of resistance = (5 N/kN) * (mass of the train in kN)
The mass of the train is given as 120 Mg (1 M = 1000 kg). Converting it to kN:
Mass of the train = (120 Mg) * (1000 kg/Mg) = 120,000 kN
Force of resistance = (5 N/kN) * (120,000 kN) = 600,000 N
Therefore, the force required for a constant speed is 600,000 N.
b) The force that causes acceleration:
The force in the drawbar is already given as 30 kN.
Therefore, the force that causes acceleration is 30 kN.
c) The acceleration:
To find the acceleration, rearrange the equation F = ma to solve for a:
a = F / m
Substituting the force causing acceleration and the mass into the equation:
a = (30 kN) / (120,000 kN) = 0.00025 m/s^2
Therefore, the acceleration is 0.00025 m/s^2.