1. Work and Energy Type Question: A rollercoaster comprises a complex path of varying slopes using a frictionless rail. The coaster begins with a 60 m powered rise, after which the carriages are released and travel the length of the track with no external power. At the track's lowest point, it is 10 m below ground level. a. What is the maximum velocity of the rollercoaster during its run. b. The highest point after the start is 55 m above ground level, where the track runs level for 20 m. How long does it take the carriages to cover this section? c. The roller coaster contains a loop which has its base at ground level. What is the maximum diameter of the loop such that the carriages will not detach from the track at the top of the loop? d. What would be the maximum g-force experienced by passengers as they travel round this loop? e. The steepest drop on the track has a gradient of 6:1. What is the acceleration at this point? f. It is discovered that over this part of the track, the cars are experiencing friction forces of 100 N. If the length of this drop is 40 m, what is the total work done on a carriage weighing 200 kg?
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.
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