An engine of mass 5000 kg pulls a train of ten trucks each of mass 2000 kg along a horizontal track. Assume that the frictional forces to be 5000 N and that the engine exerts a force of 50 000 N on the rails. If the trucks are numbered from 1 to 10 starting with the one next to the engine calculate:
(a) the net total accelerating force
(b) the acceleration of the train
(c) the force of truck 6 on truck 7
(d) the force of truck 9 on truck 8
(a) Net force = 50,000 - 5000 = 45,000 N
(b) a = (Net force)/M
where M is the total mass of train and cars, 25,000 kg
a = 1.8 m/s^2
(c) (Mass of 4 cars )*a = 14,400 N
(d) (Mass of 2 cars)*a = ?
To answer these questions, we need to first calculate the net total accelerating force, then use this value to calculate the acceleration of the train. Finally, we can determine the forces between the trucks.
(a) The net total accelerating force can be calculated by subtracting the frictional forces from the force exerted by the engine on the rails. The frictional forces are given as 5000 N. The force exerted by the engine on the rails is given as 50,000 N.
Net total accelerating force = Force exerted by engine - Frictional forces
= 50,000 N - 5,000 N
= 45,000 N
Therefore, the net total accelerating force is 45,000 N.
(b) The acceleration of the train can be calculated using Newton's second law, F = ma, where F is the net total accelerating force and m is the total mass of the train.
Mass of the engine = 5000 kg
Mass of each truck = 2000 kg
Number of trucks = 10
Total mass of the train = Mass of the engine + (Number of trucks * Mass of each truck)
= 5000 kg + (10 * 2000 kg)
= 5000 kg + 20,000 kg
= 25,000 kg
Acceleration of the train = Net total accelerating force / Total mass of the train
= 45,000 N / 25,000 kg
= 1.8 m/s^2
Therefore, the acceleration of the train is 1.8 m/s^2.
(c) The force of truck 6 on truck 7 is equal to the force of truck 7 on truck 6 because Newton's third law states that for every action, there is an equal and opposite reaction. Therefore, the force of truck 6 on truck 7 is the same as the force of truck 7 on truck 6.
(d) Similarly, Newton's third law applies to the force of truck 9 on truck 8. Therefore, the force of truck 9 on truck 8 is the same as the force of truck 8 on truck 9.
To solve these questions, we need to understand the concepts of Newton's second law of motion, the net total force, and the concept of an object exerting force on another object.
(a) To find the net total accelerating force on the train, we need to consider the forces acting on it. In this case, there are two significant forces: the frictional force and the force exerted by the engine.
The frictional force is given as 5000 N, and the force exerted by the engine is 50,000 N. Since the train is moving horizontally, there is no vertical force to consider.
The net total force is obtained by subtracting the frictional force from the force exerted by the engine:
Net total force = Force exerted by the engine - Frictional force
= 50,000 N - 5000 N
= 45,000 N
Therefore, the net total accelerating force on the train is 45,000 N.
(b) To find the acceleration of the train, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Using the formula:
Net total force = mass of the train × acceleration
We can rearrange the formula to:
Acceleration = Net total force / mass of the train
Acceleration = 45,000 N / (5000 kg + (10 × 2000 kg))
= 45,000 N / 25,000 kg
= 1.8 m/s²
Therefore, the acceleration of the train is 1.8 m/s².
(c) To calculate the force of truck 6 on truck 7, we need to understand that truck 6 exerts a force on truck 7 equal to the force necessary to accelerate truck 7.
Since the trucks are connected and moving together, the force exerted by truck 6 on truck 7 is equal to the net total force acting on truck 7.
Thus, the force of truck 6 on truck 7 is 45,000 N.
(d) To calculate the force of truck 9 on truck 8, we use the same principle as in part (c). Truck 9 exerts a force on truck 8 equal to the net total force acting on truck 8.
Thus, the force of truck 9 on truck 8 is also 45,000 N.