Transcription
A force is any push or pull. Forces can be contact forces, that's when objects are physically touching, like when you push a door, or they can be non-contact like magnetism, electrostatic forces, and gravity.
Making this distinction is pretty new to GCSE, and it's a bit silly because even contact forces are due to the electrostatic repulsion between electrons in your skin and the door, for example. But whatever. Contact forces include friction, air resistance, tension, and a normal contact force. Normal means that the force is at right angles to the surface.
The important thing is that we can represent forces with vectors. That is an arrow that shows the direction and magnitude of the force. The magnitude is the size of the force and that's indicated by the length of the arrow.
If two forces act on an object, there is a resultant force. We find this by technically adding the vectors. However, if they go in opposite directions, one must be negative. So, in this case, the resultant force would be 3 newtons to the right, and that's positive if we've decided the positive is in the right direction.
If vectors are at right angles to each other, you use Pythagoras to find the resultant. This works because you essentially have a right angle triangle if you move one of the forces.
If forces are balanced, that is they add up to zero. That means the object will not accelerate. Its velocity won't change. Note that doesn't necessarily mean it's not moving. It just stays at a constant velocity. And if that was 0 m/s to begin with, then it remains stationary. This is Newton's first law of motion, by the way. More on those in a bit.
If a measurement or quantity just has magnitude but no direction, it's not a vector, but it's called a scalar instead. Here are some examples of both. Note that displacement is distance traveled with a direction, while similarly, velocity is a vector form of speed.
Weight is just another name for the force due to gravity that acts on an object. It's calculated by multiplying the mass in kg by gravitational field strength or g. Try not to call it gravity. Here on Earth, that's 9.8 newtons per kg. Sometimes we just round that to 10, but you'll be told which to use in a question. That means that 1 kg of mass on Earth has a weight of 10 newtons or 9.8.
Now, if you hold an object up with your hand, you must be pushing up with a force that is equal to its weight in order for the forces to be balanced. So, it doesn't accelerate. However, it also means that if you lift it upwards at a constant speed, that's also true. To lift something up at a constant speed or even lower it at a constant speed, you must be pushing upwards with a force that is equal to the weight. To start lifting it upwards from rest is a different matter.
Of course, we can therefore calculate the energy that is used to lift this object using the equation for work done. Work done equals force times distance moved. Work done is just a fancy term for energy transferred by a force. This equation is true for any situation, but in this case, the force is the weight and the distance is the height. So, we could say the gain in energy is equal to mass * g * h. Does that look familiar? It should because that's the exact same equation for calculating gravitational potential energy. That's GPE change.
To be precise, forces can also deform an object, change its shape. If you pull on a spring that is fixed at one end, it will stretch or extend. Hook's law states that F = k * e. Thus, force equals spring constant, sometimes called stiffness, times extension. This works for any object that stretches elastically, that is returns to its original shape once the force is removed. It's also true if an object is compressed instead. As k is a constant, force and extension are directly proportional. That means whatever happens to one happens to the other. So double the force, we have double the extension.
To test this, we can hang slotted masses off a spring, increase the mass, re-measure every time, and you should end up with a straight line of best fit that goes through the origin. 0. And this proves this directly proportional relationship. Just make sure your ruler's zero mark is lined up with the bottom of the spring. That way, you can be sure you're only measuring extension rather than the length of the whole spring. Also, make sure you're at eye level with the bottom of the spring when measuring against the ruler to avoid parallax error.
The energy stored in a spring is equal to half ke. If something was attached to the spring and you let go, the object would gain the same amount of kinetic energy, at least in an ideal or closed system. That is no energy is lost to the surroundings due to heat.
For example, a moment is a turning force like when you turn a nut with a spanner. This is equal to force times distance to the pivot. So the unit just ends up being Newton m. Now this equation might look similar to the work done equation, but this force and distance here are perpendicular to each other rather than parallel. Like normal forces, if the moments turning clockwise are equal or balanced with the moments turning anticlockwise in the opposite direction, the object will not turn. That is if it wasn't turning to begin with. We call this the principle of moments. By the way, you need to know this definition. An application of moments is gears. A small gear can turn a large gear in order to increase the moment produced.
You can think of pressure as being how concentrated a force is. The equation is pressure is equal to force divided by area. So the unit for pressure is newtons per meter squared. We can also call this unit pascals or pa for short. You probably know the deeper you go underwater, the greater the pressure. This is due to the weight of the water above your head pushing down on you. We can calculate this pressure by using P = h * row * g. Row is just a Greek letter that looks like a P. So, it's height times density times gravitational field strength. The density of water is 1,000 kg per meter cubed.
Gas pressure is a result of the collisions between the gas particles and the surface of the container they're in. You can increase this pressure by adding more gas, reducing the volume or raising the temperature which makes the particles move faster and they collide with the walls of the container with a greater force. These result in the collisions occurring more frequently while increasing the temperature also results in the particles having more kinetic energy. So they collide with the walls with more momentum, therefore exerting a greater force. The higher your altitude, the less dense the atmosphere is. So pressure decreases.
Speed and velocity are measured in meters/s. But velocity also has a direction. So it could be positive or negative or up or down, left and right. Here are some typical traveling speeds. Speed and velocity are calculated by distance or displacement divided by time. And if you have a distance time graph, it's the gradient of the graph that gives you the speed or velocity. If it's a curve, just draw a tangent at the point you need to find the gradient for.
A speed or velocity time graph can give you even more information, though. This time the gradient gives you change in speed divided by time which is acceleration. Here's the equation a = v - u / t. That v - u is just change in velocity. Final velocity take away initial velocity. The unit of acceleration is m/s squared and it tells you how quickly speed is changing. If it's a negative gradient heading towards zero, this means the object is decelerating, slowing down. However, this graph can also go into negative values. For example, when a ball is thrown upward and comes back down. In that case, the velocity starts positive and fast but decreases to zero when it reaches the top the apex where it turns around. So then the velocity becomes more negative as it falls. Incidentally, this graph has a constant negative gradient because gravity is accelerating it downwards at a constant rate even though its direction changes. What you find is that for any object that's falling, its acceleration is 9.8 m/s squared downwards, the same as gravitational field strength because they're the same thing actually, but you don't need to know why.
A velocity time graph can give you the distance traveled as well. You get that by calculating the area under the graph. If you have any area under 0 m/s, though, that counts as negative displacement, by the way. That's why the areas of both these triangles in this graph add up to zero. That makes sense, though, doesn't it? Seeing that it's gone back from whence it came.
Newton's equations of motion or suvat are a way of predicting what an object will do if it's accelerating. S is displacement, U is initial velocity, V is final velocity, A is acceleration, and T is time. And the object will usually start at rest, stationary. So U is zero. And like we said, if an object is falling, A is the same as G. That's 9.8 or 10 m/s squared. For any question involving one of these equations, you write down your variables, put a question mark next to what you're trying to find, and put the values for the other three that you know from the question. You can ignore the fifth unused variable. Depending on what data you're given, you pick the appropriate equation with the four variables in, rearrange it if necessary, then just plug in your numbers.
We already know that Newton's first law is this. When there's no resultant force, an object's motion is constant. In other words, no change in velocity. That could be because there are no forces acting or the forces acting on it are balanced. By the way, inertia is the term we use to describe the tendency for an object's motion to stay constant unless acted on by a resultant force.
Newton's second law involves unbalanced forces. That is, there is a resultant force. This is equal to ma, mass times acceleration. That's all Newton's second law is. F = ma. Only one of these laws can be true in any situation. There's either no resultant force, Newton's first law, or there is Newton's second law.
We can prove Newton's second law by doing a practical. We use a trolley on a track being pulled by the weight of slotted masses hanging over a pulley connected by string. We can use light gates or photo gates to measure the acceleration between two points. Then change the weight on the string. Just remember that whatever mass you take off the hanger must go on the trolley afterwards. As the force here is accelerating both the trolley and the masses themselves, we draw a graph of force against acceleration and it should be a straight line through the origin proving the proportional or directly proportional relationship between force and acceleration. The gradient actually should give you the total mass of the trolley and masses.
Newton's third law however is always true and this is the one that people get confused about. Understandably though for every action that means force there is an equal and opposite reaction force. But this is not referring to balanced forces. It's all about perspective. When we think about the first two laws, we're only really considering one object. For example, the force pulling downwards on the ball is its weight. There's a resultant force downwards. However, if you zoom out and consider what's producing the weight to begin with, we know that the Earth is pulling down the ball. But Newton's third law says the complete opposite is true as well. The ball is also pulling the Earth up. Now, the Earth is so massive that it doesn't really have an effect on it, but it's still true nevertheless. Another example, if we have two ice skaters, if the guy skater pushes on the girl skater, there's an equal and opposite reaction force pushing back on him, too. That's why they both move away from where they were.
The overall stopping distance for a car is the result of thinking distance. That's how far you go before you react to seeing the bunny, for example, and the braking distance after you've slammed on the brakes. If you double your speed, you double your thinking distance because you travel twice as far in the time it takes for you to react. That makes sense. However, doubling your speed quadruples your braking distance because your car needs to lose all of its kinetic energy, which is equal to half mv squared. So that means that if you double the v * 2, if we square that, that's times 4. If you triple your speed, your kinetic energy goes up by a factor of 9. So that means so does your braking distance. Other factors that affect thinking distance are distractions, alcohol, drugs. Whereas breaking distance can be affected by the condition of your brakes, the tires, the roads, the weather, etc.
Momentum is similar to inertia. You can think of it being a measure of how hard it is to get something to stop. The equation is momentum is equal to mass times velocity. So the unit therefore is kg m/s. Momentum is a vector which means you can have negative momentum if your velocity is negative.
In a collision, total kinetic energy is very rarely conserved. That means that we will lose kinetic energy in the collision. But total momentum is always conserved. That means whatever the total momentum of the objects before the collision was, there must be the same total momentum afterwards as well. Calculations on this can be tricky, but you just have to be careful with your pluses and minuses. You write down m1*u1 if there's just one object moving to begin with. Remember u from suvat, its initial velocity. We can use it here, too. and we add m2*u2 if there's a second object moving too. This then is the total momentum before the collision. This could also be zero though if nothing's moving to begin with. Say a cannon about to fire. Then all we have to say is that this is equal to the total momentum afterwards. M1*v1 for one object plus m2*v2 if the second object is moving after two. If they're coupled together afterwards, we just say m * v where m is the total mass of the two. This is one of the few times where it's better to put your numbers in before rearranging. But we leave the variable we're trying to find as this letter. That's what we want to make the subject. Making sure that everything traveling to the left, say, has a negative velocity, and you'll be left with one unknown variable. Rearrange to find it, and you'll get your answer. Incidentally, in the case of the cannon, as there's zero total momentum before, the same must be true afterwards, too. The cannonball is moving, though, so that must mean the cannon has the same momentum, but in the opposite direction. They still add up to zero or we could say the momentum cancel each other out. This is an example of recoil.
Newton's second law says that F = ma but we know that a is equal to change in velocity over time delta V over T. So actually if we multiply that by mass we find that force is equal to change in momentum over time as well or we can say rate of change of momentum. The shorter the time taken for momentum to change the bigger the force needed or felt. That's why we use seat belts, airbags, and crumple zones in cars. If you're in a crash, your change in momentum is the same. But when we have these safety features, they increase the time taken for this momentum to be lost. So, a smaller force is felt, and you're more likely to survive. It's just two ways of looking at forces. The bigger the force, the faster the acceleration or deceleration. And so, that also means the faster the momentum changes, too.
So, I hope you found that helpful. Leave a like and a comment if you did and click on the card to take you to the playlist for all of the papers. And don't forget to check out the science shorts app to help you test your knowledge.