Explain how it is possible for a motorcycle (mass = 250 kg) to have the same momentum as a locomotive engine (mass = 2,500 kg)
i though momentum was directly proportional to mass so the more mass the more the momentum? how is it possible then?
momentum is mass * velocity
So, two objects of different masses can have the same momentum if their velocities are different.
You are correct that momentum is directly proportional to mass, and generally, an object with a larger mass would have greater momentum. However, it is possible for a motorcycle and a locomotive engine to have the same momentum if the motorcycle has a much higher velocity than the locomotive.
To understand this, we need to consider the equation for momentum: momentum = mass * velocity (p = mv). If the mass of the motorcycle is 250 kg and the mass of the locomotive engine is 2,500 kg, for them to have the same momentum, the velocity of the motorcycle must be ten times larger than that of the locomotive.
By having a much higher velocity, the motorcycle compensates for its smaller mass, resulting in the same momentum as the much larger locomotive engine. So even though the motorcycle has less mass, it can achieve the same momentum as the locomotive engine by traveling at a much higher speed.
You're correct that momentum is directly proportional to mass. According to Newton's second law of motion, momentum is the product of an object's mass and its velocity. So, in general, an object with a larger mass will have a greater momentum if its velocity is the same as another object.
However, in the given scenario, although the motorcycle and the locomotive engine have different masses, it is actually possible for them to have the same momentum if their velocities are adjusted accordingly.
Momentum is a vector quantity, which means it has both magnitude and direction. In this case, if the motorcycle has a much higher velocity than the locomotive engine, it can compensate for its smaller mass and still have the same momentum.
Let's do some calculations to illustrate this:
If we assume the motorcycle has a velocity of 100 meters per second (m/s), and the locomotive engine has a velocity of 10 meters per second (m/s), we can calculate their respective momenta.
For the motorcycle:
Momentum = mass × velocity
Momentum = 250 kg × 100 m/s
Momentum = 25,000 kg·m/s
For the locomotive engine:
Momentum = mass × velocity
Momentum = 2,500 kg × 10 m/s
Momentum = 25,000 kg·m/s
As you can see, even though the motorcycle has just one-tenth of the mass of the locomotive engine, if its velocity is ten times greater, their momenta will be the same.
So, while mass does influence momentum, it is not the only factor. Velocity also plays a crucial role in determining an object's momentum. In this case, the motorcycle can have the same momentum as the locomotive engine by having a much higher velocity.