Newton's Second Law:
As Newton’s first law states, an object will remain at rest or at constant velocity unless force is applied. Thus, when force is applied, an object will experience a change in velocity, acceleration. Newton’s second law describes motion when the sum of the forces does not equal zero. It states that:
The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.
Net force refers to “unbounded force”, force not canceled out by an opposing force. Net force is found by taking the vector sum of the forces. If the sum is zero, no net force exists. If the sum is not zero, a net force is present. For example, if an object is pulled forward with 400 N of force, and 100 N of frictional force acts against this force, then the net force is 300 N in the direction of the pulling force:
The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.
Net force refers to “unbounded force”, force not canceled out by an opposing force. Net force is found by taking the vector sum of the forces. If the sum is zero, no net force exists. If the sum is not zero, a net force is present. For example, if an object is pulled forward with 400 N of force, and 100 N of frictional force acts against this force, then the net force is 300 N in the direction of the pulling force:
Newton’s second law can be expressed by the equation:
The above can be used to find the force, in Newton’s, acting on an object. For example, if a 30kg block accelerates at a constant 3 m/s/s, then the net force acting on the block is equal to:
Thus, Newton’s second law can be used to solve for force using mass and acceleration, and conversely, to find acceleration or mass.
Newton's Second Law and Cycling:
On the Newton’s first law page, an example was given wherein a bicycle with no force applied moved at a constant velocity.
However, in real life, one cannot pedal a bicycle up to speed and coast for the remainder of the journey. Unless pedaled, a bicycle will eventually stop. This is because there is another force which always acts on a bicycle in motion. This force is friction, the force which acts to resist motion between two surfaces in contact. A bicycle's tires experience friction where they contact the road; this force acts against the forward force of pedaling. As stated, an object will always accelerate in the direction of net force. When friction is greater than the applied force (pedaling), then the bicycle will accelerate in the direction of the frictional force. When applied force is greater, then the bicycle will accelerate in the direction of applied force. When the two forces equal, then net force is equal and the bicycle is at rest or at constant velocity. The three scenarios are shown below:
However, in real life, one cannot pedal a bicycle up to speed and coast for the remainder of the journey. Unless pedaled, a bicycle will eventually stop. This is because there is another force which always acts on a bicycle in motion. This force is friction, the force which acts to resist motion between two surfaces in contact. A bicycle's tires experience friction where they contact the road; this force acts against the forward force of pedaling. As stated, an object will always accelerate in the direction of net force. When friction is greater than the applied force (pedaling), then the bicycle will accelerate in the direction of the frictional force. When applied force is greater, then the bicycle will accelerate in the direction of applied force. When the two forces equal, then net force is equal and the bicycle is at rest or at constant velocity. The three scenarios are shown below:
Finding Net Force:
A rider pedals a bicycle along flat ground with an acceleration of 2 m/s/s. The bicycle mass of the bicycle is 30kg. What is the net force on the bicycle?
To solve this problem, create a free body diagram representing the forces acting on the bicycle:
To solve this problem, create a free body diagram representing the forces acting on the bicycle:
Now, take the sum of the forces in each direction:
The bicycle is not accelerating in the Y direction. Based on Newton’s first law, it can be thus determined that the sum of the forces is zero. The bicycle is accelerating in the X direction. To find net force, we must first solve for the force of the rider and the force of friction.
The force of the rider is equal to mass times acceleration, as below:
The force of the rider is equal to mass times acceleration, as below:
Next, find the frictional force. Frictional force is equal to a constant, mu, multiplied by the normal force. The value of mu is determined by the identity of the two surface is contact. In this case, the surfaces are the rubber of the tires and the asphalt of the road. Assume mu is equal to 0.2 .
Normal force is equal and opposite the force of gravity. The normal force is equal to the mass of an object multiplied by acceleration due to gravity:
Normal force is equal and opposite the force of gravity. The normal force is equal to the mass of an object multiplied by acceleration due to gravity:
Now, solve for friction:
To find the net force, substitute the values for friction and applied force into the equation for sum of the forces in x:
The net force on the bicycle is 91.2 in the direction of the applied force. Thus, Newton’s second law can be used to solve for force, or for mass or acceleration, in a variety of real life scenarios, including cycling.