A cylinder of mass $10 \,kg$ is rolling on a rough
Question:

A cylinder of mass 10kg10 \,kg is rolling on a rough plane with a velocity of 10m/s10 \,m/s. If the coefficient of friction between the surface and cylinder is 0.50.5, then before stopping it will cover a distance of (Take g=10m/s2g = 10\, m/s^2):

Updated On: Jun 20, 2022
  • 10 m
  • 7.5 m
  • 5 m
  • 2.5 m
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The Correct Option is A

Solution and Explanation

Kinetic energy of cylinder is consumed in doing work against friction in rolling motion.
A body of mass mm moving with velocity vv, Possess kinetic energy given by
K=12mv2(1)K=\frac{1}{2} m v^{2} \ldots(1)
This kinetic energy is utilized in doing work against the frictional forces.
W=μmgs(2)W=\mu m g s \ldots(2)
Where μ\mu is coefficient of kinetic friction, mm is mass, gg is gravity and ss is displacement.
Equating Egs. (1) and (2)(2), we get
12mv2=μmgs\frac{1}{2} m v^{2}=\mu m g s
Where 12mv2=12×10×(10)2\frac{1}{2} m v^{2}=\frac{1}{2} \times 10 \times(10)^{2}
=500kgm/s=500\, kg - m / s
Given, v=10m/s,μ=0.5,m=10kgv=10 \,m / s, \mu=0.5, m=10\, kg
g=10m/s2g=10\, m / s^{2}
s=12×m×(10)2μmg\Rightarrow s=\frac{\frac{1}{2} \times m \times(10)^{2}}{\mu mg }
=500.5×10=10m=\frac{50}{0.5 \times 10}=10 \,m
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Concepts Used:

Work, Energy and Power

Work:

  • Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
  • The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.

Energy:

  • A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
  • There are two types of mechanical energy such as; Kinetic and potential energy.

Read More: Work and Energy

Power:

  • Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
  • Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.