Kinematics
A machine is a device that accepts energy in some available form and utilizes it to do a type of work. Energy, work, or power has to be transferred from one mechanical part to another to run a machine. While the transfer of energy between two machine parts, those two parts experience a relative motion with each other. Studying such relative motions is termed kinematics.
Kinetic Energy and Work-Energy Theorem
In physics, work is the product of the net force in direction of the displacement and the magnitude of this displacement or it can also be defined as the energy transfer of an object when it is moved for a distance due to the forces acting on it in the direction of displacement and perpendicular to the displacement which is called the normal force. Energy is the capacity of any object doing work. The SI unit of work is joule and energy is Joule. This principle follows the second law of Newton's law of motion where the net force causes the acceleration of an object. The force of gravity which is downward force and the normal force acting on an object which is perpendicular to the object are equal in magnitude but opposite to the direction, so while determining the net force, these two components cancel out. The net force is the horizontal component of the force and in our explanation, we consider everything as frictionless surface since friction should also be calculated while called the work-energy component of the object. The two most basics of energy classification are potential energy and kinetic energy. There are various kinds of kinetic energy like chemical, mechanical, thermal, nuclear, electrical, radiant energy, and so on. The work is done when there is a change in energy and it mainly depends on the application of force and movement of the object. Let us say how much work is needed to lift a 5kg ball 5m high. Work is mathematically represented as Force ×Displacement. So it will be 5kg times the gravitational constant on earth and the distance moved by the object. Wnet=Fnet times Displacement.
(a). You are required to design a roller coaster with the profile shown in Figure Q2(a).
An electric motor will pull the coaster to the top of the first hill. After the coaster has been pulled to the top, no more external work will be added to it. Hint: the amount of energy the coaster has to complete its journey on the track depends on the potential energy on the first hill. This will give you the relationship between the height of this hill and the speed of the coaster.
The shape of the first hill will determine if the coaster will safely travel on the track and speed of the coaster. Hint: you can imagine the coaster as a particle that moves in space along the track in a projectile motion.
The coaster exit through a second hill to maintain feeling of speed and thrill in the ride. The second hill is also to maintain the speed to the next stage of the ride. Hint: the safety of travel on the track depends on the speed you are travelling and is related to the hill you are coming from.
Instead of adding a loop to your coaster, the coaster is allowed to gradually cruise to a stop. Assume is a flat path.
Assuming a total mass of 1000kg, explain with calculations how would you design the roller coaster from start till the end of coaster ride:
(i) the power of the electric motor to pull the coaster up the first hill.
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