A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )
A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )
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- $0.2$
- $0.4$
- $0.5$
- 0.3
The Correct Option is B
Approach Solution - 1
\(a=-\mu g\)
\(\because v=u+at\)
\(0=20+(\mu\times10)\times5\)
\(50\mu=20\)
\(\mu=\frac{2}{5}\)
=0.4
Therefore , the value of coefficient of friction is 0.4
So , the correct option is (B) : 0.4
Approach Solution -2
The work done by the frictional force is equal to the change in kinetic energy.
The frictional force \( f = \mu \times N = \mu \times mg \), where \( \mu \) is the coefficient of friction, \( m \) is the mass, and \( g \) is the acceleration due to gravity.
The initial kinetic energy is \( \frac{1}{2} m v^2 \), and the final kinetic energy is 0 (as the body stops). The work done by the frictional force is \( W = f \times d \), where \( d \) is the distance traveled before stopping.
From the equation of motion \( v_f = v_i + a t \), with \( v_f = 0 \), \( v_i = 20 \, \text{m/s} \), and \( t = 5 \, \text{s} \), we can find the acceleration \( a = \frac{v_f - v_i}{t} = \frac{0 - 20}{5} = -4 \, \text{m/s}^2 \).
Using \( F = ma \), the frictional force is \( F = 10 \times (-4) = -40 \, \text{N} \).
Now, using \( F = \mu mg \), we get:
\[ \mu = \frac{40}{10 \times 10} = 0.4 \]
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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.