why is net force a vector sum

When you get a paycheck, there are two numbers to look at. First is the
gross amount you earn, which is the total amount of money you make. So if you make $50,000 a year, this would be reflected in the gross earnings of your check. The second number to take note of is the net amount, which is the amount you actually take home. A net amount is the difference between the gross amount and any deductions. In the case of your paycheck, this may come in the form of taxes, insurance premiums, retirement funds, and any other deductions that come out of your total gross earnings. The same idea is true for net force. This is the vector sum of all forces acting on an object. As we learned in another lesson, forces are vector quantities because they have both magnitude and direction. We represent vectors with arrows - the size of the arrow shows the relative magnitude of the force, while the direction of the arrow shows in which direction the force is acting. Because forces have different magnitudes and directions, we can't just add up the forces and get a total amount. What we have to do is find the difference between the forces as we add up the vectors - we have to find the net force. This is quite similar to adding positive and negative numbers. For example, if there is a force acting on an object and it is 5 Newton (capital letter 'N' for Newton) to the left, we could see this as +5 to the left. If at the same time there is a 5 N force to the right acting on that same object, this would be like subtracting 5 to the right. 5 - 5 = 0, so we have zero net force. The forces cancel each other out. Forces don't always cancel out, though. For example, if there are two forces acting toward the right, and they are both 5 N, then we have 5 + 5 = 10. This would be 10 N to the right because both forces are acting in the same direction with the same magnitude. But let's say we have 5 N to the right and 15 N to the left. 15 - 5 = 10, and since the greater magnitude force is acting to the left, that's where our net force is, too. So in this case, the net force is 10 N to the left. We can do this for vertical forces as well. Say that an object is falling toward the ground, which means that both gravity and air resistance are acting on it.


If gravity is pulling down with 600 N and air resistance is pushing up with only 200 N, then 600 - 200 = 400, so we have 400 N downward as our net force. Newton's first law says that an object continues in its state of rest or motion unless acted on by an outside unbalanced force. Forces are unbalanced when there is a net force greater than zero. When there is no net force, we say the forces are balanced. This can be true for both moving and stationary objects. For example, an airplane traveling at constant velocity (so both constant speed and direction) can have balanced forces acting from the front and the back. The plane is moving, but if both forces are the same magnitude, then there is zero net force and the plane will continue traveling along that path until there is a net force. When the net force of an object is zero, we say it is in equilibrium, a state of 'no change. ' Net force can be written out mathematically, but we can also create a visual representation of the forces acting on an object. We do this through free-body diagrams, which are force-vector diagrams. You already know that vectors have both magnitude and direction and are represented by arrows. In free-body diagrams, the size of the arrow still indicates the magnitude, and the direction of the arrow tells us which way the force is acting. But now we also have the object, which is represented by a box, and the forces acting on the object come out from its sides. If you have been reading through Lessons 1 and 2, then ought to be thoroughly understood. An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an. In the statement of Newton s first law, the unbalanced force refers to that force that does not become completely balanced (or canceled) by the other individual forces. If either all the vertical forces (up and down) do not cancel each other and/or all horizontal forces do not cancel each other, then an unbalanced force exists. The existence of an unbalanced force for a given situation can be quickly realized by looking at the free-body diagram for that situation.


Free-body diagrams for three situations are shown below. Note that the actual magnitudes of the individual forces are indicated on the diagram. In each of the above situations, there is an unbalanced force. It is commonly said that in each situation there is a net force acting upon the object. The is the vector sum of all the forces that act upon an object. That is to say, the net force is the sum of all the forces, taking into account the fact that a force is a vector and two forces of equal magnitude and opposite direction will cancel each other out. At this point, the rules for summing vectors (such as force vectors) will be kept relatively simple. Observe the following examples of summing two forces: Observe in the diagram above that a downward vector will provide a partial or full cancellation of an upward vector. And a leftward vector will provide a partial or full cancellation of a rightward vector. The addition of force vectors can be done in the same manner in order to determine the net force (i. e. , the vector sum of all the individual forces). Consider the three situations below in which the net force is determined by summing the individual force vectors that are acting upon the objects. A Net Force Causes an Acceleration, a net force (i. e. , an unbalanced force) causes an acceleration. In a previous unit, several means of representing accelerated motion (position-time and velocity-time graphs, ticker tape diagrams, velocity-time data, etc. ) were discussed. Combine your understanding of acceleration and the newly acquired knowledge that a net force causes an acceleration to determine whether or not a net force exists in the following situations. Click on the button to view the answers. 1. Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Click the buttons to view the answers. 2. Free-body diagrams for four situations are shown below. The net force is known for each situation. However, the magnitudes of a few of the individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown forces. Then click the button to view the answers.

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