Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
A body has a mass of 10 kg. How much work must be done to raise its speed from 2 m/s to 6 m/s?
120 J
160 J
180 J
200 J
160 J
The work required to change the speed of an object is equal to the change in its kinetic energy, as stated by the Work-Energy Theorem. For a mass of 10┬аkg moving from 2┬аm/s to 6┬аm/s, the work done is 160┬аJ.
The work required to change the speed of an object is equal to the change in its kinetic energy, as stated by the Work-Energy Theorem. For a mass of 10┬аkg moving from 2┬аm/s to 6┬аm/s, the work done is 160┬аJ.
Think of pushing a bicycle; it takes much more physical effort to accelerate from a slow roll to a fast sprint than it does to maintain a constant speed.
WKE: Work equals Kinetic change
W=╬ФK=21тАЛm(vf2тАЛтИТvi2тАЛ) тАФ Work-Energy Theorem
K=21тАЛmv2 тАФ Kinetic Energy formula
According to the Work-Energy Theorem, the net work done on an object equals the change in its kinetic energy. Kinetic energy is defined as K=21тАЛmv2. The work done is calculated as ╬ФK=21тАЛm(vf2тАЛтИТvi2тАЛ). Substituting the given values: 21тАЛ├Ч10├Ч(62тИТ22)=5├Ч(36тИТ4)=5├Ч32=160┬аJ.
Work is a scalar quantity measured in Joules (J).
Kinetic energy depends on the square of the velocity, meaning speed changes have a non-linear effect on energy requirements.
The Work-Energy Theorem is valid for both constant and variable forces.
Provides a direct method to find energy changes without calculating force or acceleration time.
Does not account for non-conservative forces like friction unless specified.
Determining braking distance of vehicles.
Designing mechanical flywheels.
Initial kinetic energy: 21тАЛ├Ч10├Ч22=20┬аJ.
Final kinetic energy: 21тАЛ├Ч10├Ч62=180┬аJ.
Option A (120 J) is incorrect as it results from simple linear subtraction without squaring the velocity.
Option C (180 J) is the final kinetic energy, not the change in energy.
B is correct тАФ The work done is equal to the change in kinetic energy, which is 180┬аJтИТ20┬аJ=160┬аJ.
Always remember to square the velocity values separately before subtracting when dealing with kinetic energy changes; common mistakes involve calculating (vfтАЛтИТviтАЛ)2 instead of vf2тАЛтИТvi2тАЛ.