Force and Mass - Acceleration?

In summary, the Crampton coal-fired train engine built in 1852 had a mass of 48.3 tonnes and a force capability of 22.4 kN. Assuming it was pulling train cars twice its own mass and experiencing a friction of 10.1 kN, the acceleration of the train would be 0.0849 m/s^2. This may seem slow, but in only 100 seconds the train would be traveling over 8 m/s.
  • #1
thua
9
0
When the Crampton coal-fired train engine was built in 1852, its mass was 48.3 t (1.0 t = 1.0 x 10^3 kg) and its force capability was rated at 22.4 kN. Assuming it was pulling train cars whose total mass doubled its own mass and the total friction on the engine and cars was 10.1 kN, what was the magnitude of the acceleration of the train?
What I have: (not sure if it's right though)
m = 48.3 t = (48.3 x 10^3 kg) x 3 = 144.9 x 10^3 kg
net force = 22.4kN - 10.1 kN = 12.3 kN = 12300 N
acceleration = ?
acceleration = net force / mass
= 12300 N / 144.9 x 10^3 kg
acceleration = 0.0849 m/s^2
acceleration = 8.49 x 10^3 kg
Is this right? because 0.0849 m/s^2 doesn't seem very reasonable to me. If it's wrong, could someone please help?
 
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  • #2
Your procedure looks perfectly fine to me.
 
  • #3
Were you expecting a train in 1852 to take off really fast?

Notice that in only 100 seconds (1 min 40 seconds), the train will be traveling over 8 m/s. Now that's a pretty good pace!

By the way:
"acceleration = 0.0849 m/s^2" is correct.

"acceleration = 8.49 x 10^3 kg" is nonsense. I presume you meant
"8.49 x 10^(-2) m/s^2".
 
  • #4
Yah, trains back then could go... 40mph at the most probably back then.
 

1. What is the relationship between force, mass, and acceleration?

The relationship between force, mass, and acceleration is described by 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. This means that as the force acting on an object increases, its acceleration also increases, and as its mass increases, its acceleration decreases.

2. How do you calculate force given mass and acceleration?

The formula for calculating force is F = ma, where F is the force in Newtons (N), m is the mass in kilograms (kg), and a is the acceleration in meters per second squared (m/s^2). To calculate force, simply multiply the mass by the acceleration.

3. What is the unit of measurement for force, mass, and acceleration?

The unit of measurement for force is Newton (N), for mass it is kilogram (kg), and for acceleration it is meters per second squared (m/s^2).

4. How does the acceleration of an object change when the force acting on it changes?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it. This means that as the force acting on an object increases, its acceleration also increases. Similarly, if the force acting on an object decreases, its acceleration will also decrease.

5. Can an object with a larger mass have the same acceleration as an object with a smaller mass?

No, according to Newton's Second Law of Motion, the acceleration of an object is inversely proportional to its mass. This means that if two objects are experiencing the same force, the object with a larger mass will have a smaller acceleration compared to an object with a smaller mass.

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