Let us assume that our reference frame is an inertial frame. Newton's second and third laws are valid in all inertial reference frames.
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass.
Unbalanced forces cause acceleration.
The net force is the vector sum of all forces acting on the object.
In algebraic form we write Newton's second law as
F = ma.
This is a vector equation. It is equivalent to the three equations, Fx = max, Fy = may, Fz = maz. The acceleration a = F/m is in the direction of the force and proportional to the magnitude of the force. The mass of an object is a measure of its inertia, its resistance to changing its state of motion. If two objects are supposed to have the same acceleration, then the more massive object must be acted on by a larger force, while the less massive object must be acted on by a smaller force. The mass is a scalar quantity.
Units: In SI units, mass is measured in kg, acceleration
in m/s2 and force in Newton (N).
1N
= 1 kg·m/s2.
In the British engineering system the unit of force is the pound (lb).
(See more here.)
Given the same push or pull, larger masses accelerate less than smaller masses. You need much less force to accelerate a tricycle than to accelerate a car. Because of its inertia, you need a force to accelerate an object. If there is no net force acting on an object, it will not accelerate, its velocity will not change. If it is initially at rest, it will stay at rest, if it is moving with a given speed in a certain direction, it will keep on moving with the same speed in the same direction.
Link:
 | The Truck and the Ladder |
| A force F, applied to an object of mass m1, produces an
acceleration of 3m/s2. The same force, applied to a second
object of mass m2 produces an acceleration of 1m/s2. (a) What is the value of the ratio m1/m2? (b) If m1 and m2 are combined, find their acceleration under the action of the force F.
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| A 3 kg mass undergoes an acceleration given by a = (2i + 5j)m/s2.
Find the resultant force F and its magnitude.
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| A heavy freight train has a mass of 15000 metric tons. If the
locomotive can exert a pulling force of 750000N, how long does it take to
increase the speed from 0 to 80km/h?
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| Suppose a truck loaded with sand accelerates at 0.5m/s2 on a
highway. If the driving force on the truck remains constant, what
happens to the truck's acceleration, if its trailer leaks sand at a constant
rate through a hole in its bottom?
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Assume you are standing on a 20 m high platform with a ball in your outstretched hand. At t = 0 you let go of the ball and it starts falling towards the ground below. At t = 0 the ball has zero velocity. At some later time, but before it hits the ground, its velocity is in the downward direction. Its speed is increasing as it falls. The ball is accelerating. Why is a falling ball accelerating? Which force is acting on it?
The force of gravity is acting on the falling ball. On the surface of the earth, the direction of this force is always downward, towards the ground. It pulls on all objects with mass.
As the object gains speed, other forces also act on it. The direction of the drag force (air friction) acting on the moving object is opposite to the direction of the object's velocity. The drag force tries to slow down the object. The magnitude of the drag force depends on the shape of the object, its speed, and the medium in which it is moving. For many smooth, dense objects the magnitude of the drag force at low speeds in air is very small compared to the gravitational force and we can safely neglect it.
Assume we are dropping two smooth, spherical objects of different masses, such as a bowling ball and a marble, at the same time. If the force of gravity acting on the two objects had the same magnitude, then the bowling ball would accelerate less and gain less speed in the same amount of time. The marble would hit the floor first. In an experiment, however, the two objects hit the floor at the same time. They gain the same speed in the same time. This mean that the force of gravity acting on the bowling ball must have a greater magnitude than the force of gravity acting on the marble. The force of gravity acting on an object must be proportional to the mass of the object. We write
Fg = mg.
We also have Fg = ma from Newton's second law, so g = a. The proportional constant g is called the acceleration due to gravity. On the surface of the earth g = 9.8m/s2 and its direction is downward. The force of gravity acting on an object is called its weight.
On the surface of the earth all objects experience the same acceleration due to gravity in the downward direction, regardless of their mass. The acceleration due to frictional forces is always in the direction opposite the object's velocity, and differs from object to object. However, when we are justified to neglect friction, then we can say that all dropped objects accelerate at the same rate.
Links:
| The Elephant and The Feather - Free Fall |
| The Elephant and The Feather - with Air Resistance |
Mass and weight are different quantities. Mass is a scalar. It is an inherent property of an object, independent of where and how it is measured. It tells us how hard it is to accelerate the object. Weight is a vector. It is the gravitational force acting on the object. It depends on the location of the object. On the surface of the moon the weight of an object points towards the center of the moon and its magnitude is approximately 1/6 the magnitude of its weight on the surface of the earth. The mass of the object, i.e. its resistance to acceleration, is the same everywhere. The magnitude of the gravitational acceleration is therefore smaller on the surface of the moon than on the surface of the earth. If you drop an object near the surface of the moon, its velocity changes less rapidly then the velocity of a similar object dropped near the surface of the earth.
| A pitcher throws a baseball of weight 1.4N with velocity v = 32i
m/s by uniformly accelerating her arm for 0.09s. If the ball starts
from rest, (a) through what distance does the ball accelerate before its release? (b) What vector force does she exert on it?
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| A car with a mass of 850kg is moving to the right with a constant speed of
1.44m/s. (a) What is the total force on the car? (b) What is the total force on the car if it is moving to the left?
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Link:
| Racing Balls |
In the British engineering system the unit of force is the pound (lb). The weight of an object is the gravitational force acting on the object and it is measured in lb. The unit of acceleration is ft/s2. The unit of mass is slug. We have lb = slug×ft/s2. In everyday language the mass of an object in British units is seldom referred to correctly. It is important that in physics we properly distinguish between mass and weight.
Link:
| Unit Converter 1 |
| Unit Converter 2 |
Links to other Web materials:
| Lesson 3: Newton's 2nd law of motion |
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If 
is
constant and negative, i.e.
is not
constant, but increases with time, since a is increasing and m is decreasing.
We have m = m0 - bt.
Therefore