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.
Q1
Is positive or negative work done by a constant force −→F on a particle during a straight-line displacement −→d if (a) the
angle between −→F and −→d is 30◦
; (b) the angle is 100◦
; (c) −→F = 2ˆi − 3ˆj and −→d = −4ˆi? [2+2+2]
Q2
A force −→F = (cx − 3.00x
2
)ˆi acts on a particle as the particle moves along an x axis, with −→F in newtons, x in meters,
and c a constant. At x=0, the particle’s kinetic energy is 20 J; at x = 3.00 m, it is 11 J. Find c. [5]
Q3
What is the spring constant of a spring that stores 25 J of elastic potential energy when compressed by 7.5 cm? [2]
Q4
The figure below shows a plot of potential energy U versus position x of a 0.200 kg particle that can travel only along
an x axis under the influence of a conservative force. The graph has these values: UA = 9.00J, UC = 20.00J, and
UD = 24.00J. The particle is released at the point where U forms a potential hill of height UB = 12.00J, with kinetic
energy 4.00 J. What is the speed of the particle at (a) x = 3.5 m? What is the position of the turning point on (b)
the right side and (c) the left side? [2+2+2]
Q5
A rope is used to pull a 3.57 kg block at constant speed 4.06 m along a horizontal floor. The force on the block from
the rope is 7.68 N and directed θ = 15.0
◦ above the horizontal. What are (a) the work done by the rope’s force, (b)
the increase in thermal energy of the block-floor system, and (c) the coefficient of kinetic friction between the block
and floor? [2+2+2]
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