NEWTON'S 2nd LAW OF MOTION
Here is a reminder of Newton's 2nd law:
"The force is equal to the mass times the acceleration."
What is Mass and Acceleration?
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In Newton's second law, we mention mass and acceleration, but what do these words mean?
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Mass [2]
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The mass of an object is how much matter it has, which means how much stuff it has, i.e. how many protons, electrons and neutrons an object has. The mass is a fundamental property and it is very different to the weight of an object.
The weight of an object is due to the force of gravity, meaning if you were to fly to another planet that had a different gravitational field strength to Earth, an object from Earth may weigh more or less on that planet than it did at home. However, the mass is not affected by the force of gravity, so the object will have the same mass as it did on Earth.
Acceleration [3]
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The acceleration is the rate at which an object's velocity is changing.
Moving really fast doesn't necessarily mean that an object is accelerating because it may be moving at a constant speed, which we have learned means that the forces are balanced and therefore, the object can not be accelerating.
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The direction of acceleration depends on how the object's velocity is changing, i.e whether it is slowing down or speeding up.
How Does the Mass and Acceleration Affect the Force?
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If we look at the equation given in Newton's second law:
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f = m x a
force
mass
acceleration
This equation tells us that the force depends on both the mass and the acceleration.
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Objects with fixed masses:
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If the mass stays the same, the acceleration will determine the force. This means for an object with a certain mass, a large acceleration will correspond to a large force and a small acceleration will correspond to a small force.
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We can also look at this the other way and say that if we have an object with a fixed mass, the force that we apply will determine the acceleration of the object. This means that if we apply a large force, the object will be given a large acceleration and if we apply a small force, the object will be given a small acceleration.
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Two objects with different masses:
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Now, let's look at the case where we have two objects and they both have different masses.
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If we apply the same force to an object with a large mass and an object with a small mass, they will move off with different accelerations.
The object with the large mass will move off with a smaller acceleration than the object with the small mass. This is because we have applied the same force to both of them.
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The reason for this is that we need the right hand side of the equation to be the same as the left hand side. This basically means that the number we get for the mass times the acceleration has to be the same number we have for the force. So for the right hand side to be the same as the left hand side, the case with the larger mass must have a smaller acceleration, and the case with the smaller mass must have a larger acceleration. This way both sides of the equation stay equal [1].
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If we wanted both objects to move off with the same acceleration, then we would have to apply a larger force to the object with the larger mass.
f = m x a
Newton's 2nd Law Simulation
This is explained in this simulation where a girl kicks a football and a bowling ball with the same force.
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Bowling ball = large mass
Football = smaller mass
How Does Newton's 2nd Law Apply to Rockets?
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When a rocket is launching, we want to apply a force to it so it can accelerate up into the sky.
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In a rocket launch, the mass of the rocket will be fixed, so the force we apply to the rocket will determine how large the acceleration will be.
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We will want to give the rocket a large acceleration, so according to Newton's 2nd law, we must apply a large force.
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