To calculate the coefficient of sliding friction, we can start by using the work-energy principle.
-
Calculate the initial kinetic energy (KE) of the body: \[ KE = \frac{1}{2} m v^2 \] where \( m = 20 , \text{kg} \) and \( v = 3 , \text{m/s} \).
\[ KE = \frac{1}{2} \times 20 , \text{kg} \times (3 , \text{m/s})^2 = \frac{1}{2} \times 20 \times 9 = 90 , \text{J} \]
-
Calculate the work done by friction (W_f): The work done by friction is equal to the change in kinetic energy (which is the initial KE since the final KE is 0 when the body comes to rest). Since this work is negative (it reduces the kinetic energy), we have:
\[ W_f = -KE = -90 , \text{J} \]
-
Calculate frictional force (F_f): The work done by friction can also be expressed as: \[ W_f = F_f \times d \] where \( d = 25 , \text{m} \).
Since \( W_f = -90 , \text{J} \), we can write: \[ -90 = F_f \times 25 \] Thus, \[ F_f = \frac{-90}{25} = -3.6 , \text{N} \] (The negative sign indicates that the force is acting opposite to the direction of motion, but we will consider the magnitude for our calculations).
-
Calculate the normal force (N): Since the body is on a horizontal floor, the normal force (N) is equal to the weight of the body, which can be calculated as: \[ N = m \times g = 20 , \text{kg} \times 10 , \text{m/s}^2 = 200 , \text{N} \]
-
Calculate the coefficient of friction (\(\mu\)): The frictional force can also be expressed in terms of the coefficient of friction: \[ F_f = \mu N \] Now substituting the values we have: \[ 3.6 = \mu \times 200 \] Solving for \(\mu\): \[ \mu = \frac{3.6}{200} = 0.018 \]
Thus, the coefficient of sliding friction is: \[ \mu \approx 0.018 \]