 We've learnt that if there's zero net force on an object, then there's zero acceleration, and an object will remain at rest or moving at constant velocity. But what happens if there is a net force? The object will accelerate. Let's quantify this. Newton's second law tells us that the net force acting on an object is equal to its mass times its acceleration. The net force means the sum of all the forces acting on an object. Newton's first law that we've spoken about is really just a special case of this second law. If the net force is zero, then the acceleration is zero, and an object will remain at rest or moving with constant velocity. F is a vector, that is, it has a direction, as well as a magnitude. And A, the acceleration, is also a vector. It is pointed in the same direction as the net force. The unit of force is called a Newton, or capital N for short. The units on both sides of an equation must match. On the right-hand side, we have mass, which has units of kilograms, and acceleration, which has units of meters per second squared. And therefore, the units of force, one Newton, must be a kilogram meter per second squared. Now we're going to quantify some of the forces that we introduced in the last video. The weight force, which we'll call FG, is equal to M times G. Note this M is the same mass as in F equals MA. Little G is the acceleration due to gravity on Earth, which is approximately equal to 9.8 meters per second squared. This would be different if you were on a different planet, or the moon. We can calculate the weight force for a person. Let's say the mass is 65 kilograms. Then the weight force is equal to 637 Newtons. Now because our first two quantities, M and G, were only given to two significant figures, we should only give our answer to two significant figures as well. The force due to a spring is equal to minus kx. Here k is the spring constant, and this will vary depending on the size and material that the spring is made from. And x is the displacement of the end of the spring from its unstretched position. The minus sign is there because both F and x are vectors, but they are in opposite directions. X points in the direction that the spring was extended or compressed, back to the original position of the spring. We can compare the spring force from two springs, one stretchy with a small spring constant, and one stiffer with a larger spring constant. If we stretch both springs by 10 centimeters, what will a spring force be? To calculate the forces, we first need to remember to convert everything to SI units, so 10 centimeters becomes 0.1 meters. It's a good idea after doing a calculation to check if your answer makes sense. Here we found that the stretchy spring exerts a force of 5 newtons, and the stiff spring exerts a force of 50 newtons. This makes sense. The stretchy spring doesn't pull back very much, and the stiff spring pulls back a lot. The frictional force on a moving object is equal to mu k times n, where mu k is the coefficient of kinetic friction, which depends on what the two surfaces are that are sliding against each other, and n is the normal force that we introduced last video. Friction partly arises from the roughness of surfaces. If you zoom in it might look something like this. But a large part of friction actually arises from molecules in the two objects adhering to each other. Because of the complicated nature of how friction arises, the equation that we've written here is really only an approximation for describing the frictional force, but it does generally work pretty well. For stationary objects, the frictional force is less than or equal to mu s times n. Here mu s is the coefficient of static friction. Mu s is usually greater than mu k. You can see that the main difference between these two equations is the less than or equal sign for the stationary friction. If you imagine you have a really heavy box sitting on the floor, and you apply a small force, the box doesn't move because friction applies an equal and opposite small force. You then apply a large force to the box, and it still doesn't move, because the friction force exactly opposes the large force you apply. You can see in this case for a stationary object, the frictional force varies depending on what the applied force is. But the static friction is always less than mu s n. Once the applied force is greater than mu s n, the object will accelerate, and the frictional force will be given by the equation for moving objects.