Calculations
In order to find the actual physics components of our simple machines, we had to use the following equations:
- velocity = change of distance/change of time
- acceleration = change of velocity/change of time
- force = (mass)(acceleration)
- work = (force)(distance)
Velocity
Acceleration
Velocity is the rate of distance covered, but because its a vector quantity, it must be calculated in a certain direction. In order to calculate it I timed how long it for whatever I was measuring, in the case a ball, to fall and how far the object fell. The ball I was measuring fell 0.06m down in 0.19 seconds, so I divided 0.06 by 0.19 to get .32m/s as the velocity.
Acceleration is the rate of change in velocity, or how much something is speeding up or slowing down. To find the acceleration of something, the ball, I have to divide the velocity by the time again. So, I already knew the velocity was 0.32m/s from previous calculations, so I divided that by the time, 0.19, to get 1.7m/s/s as the acceleration.
Force
Work
Force is the push or pull of an object. To determine the force of an object you multiply the mass of the object and the acceleration the object is moving at. I calculated the force of a lever with a ball in it. The lever including the ball had a mass of 0.6671kg and it fell at the rate of acceleration due to gravity, 9.8m/s/s, so I multiplied the two values together to get a force of about 0.65N.
Work is the amount of energy put into something. In order to evaluate the work you must multiply the force an object is putting in and the distance. I had previously calculated the force of my lever, which was 0.65N. I then multiplied it by the distance the lever fell, which was about 0.1m, to get 0.065J of work.
Mechanical Advantage
There are two types of mechanical advantage, real and ideal. Mechanical Advantage Real, or MAr, is how much easier, or less force, a tool makes a task. This can be calculated by dividing the force the load exerts by the F of the effort being put into the moving or effecting the load. Mechanical Advantage Ideal, or MAi, is different because it's how much further, or more distance you have to push due to using a tool. The equation to find this value is the the distanced covered by whatever force is putting in effort divided by the distance the load being effected by the load covers. However, both values don't have units because they are ratios. I will determine the MAr and MAi for an imaginary pulley as an example. Let's say this pulley has a rope that is 12m long and is being used to pull a 30N weight. In this situation, I have to pull the rope 9m with a force of 10N to raise the load 3m. In order to calculate the MAr I must divide the force I would put in without the machine, which is 30N because that's how much the weight weighs, by the force I actually put in, which was 10N. I would then get 3 as the MAr. Then to find the MAi I must divide the distance I covered, which was 9m, by the distance the load covered, which was 3m. I would then get a resultant of an MAi of 3.
Energy
There are two main types of energy, potential and kinetic. Potential energy, or PE, is the energy an object has due to its position at a height. The equation for this value is mass of the object, multiplied by acceleration due to gravity, multiplied by its height. The higher the object, the faster it falls because it has more time to accelerate, so it has a higher potential energy. It's potential because the ball hasn't fallen yet. But when the ball begins to fall the potential energy decreases as the kinetic energy increases. Kinetic energy, or KE, is the energy an object has due to motion. To compute this you divide the mass of the object by two and then multiply that quotient by the velocity of the falling object squared. When an object has it's highest PE, its KE is 0 because the ball isn't moving. But when an object has its highest KE, its PE is 0 because it no longer has any height because an object has it's highest KE right before it hits the floor. For example, let's say I dropped a ball with a mass of 100kg 10 meters. To find the PE I would multiply the mass, 100kg, by the acceleration due to gravity, 9.8m/s/s. I would then get a product of 980. I would then multiply that by the height, 10m, to get a PE of 9,800J. However to find the KE I would divide the mass, 100kg, by 2. I would have a quotient of 50kg. I would then have to find the final velocity of the ball falling. I have mentioned before that the equation for finding velocity is change of distance, 10m, divided by change of time which would be about 1.41 seconds, so I would get an average velocity of about 7m/s, but I need the final velocity. Because the ball starts with a velocity of 0 the average velocity, 7m/s, should be half of the final velocity. So I multiply that by 2 and get 14m/s as the velocity. I would then square that velocity of 14m/s to get 196m/s and multiply that by 50kg to get a KE of 9,800J which is equal to the PE of 9,800J.