The coefficient of dynamic friction is 0.05.
To find the coefficient of dynamic friction, we need to use Newton's second law of motion and the equation for friction.
Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration:
F = m * a
In this case, the body is moving along the footpath with uniform velocity, which means the acceleration is zero. Therefore, the net force acting on the body is also zero.
The force equation for friction is given by:
f = μ * N
where f is the force of friction, μ is the coefficient of friction, and N is the normal force.
In this case, since the body is moving with uniform velocity, the normal force is equal to the gravitational force acting on the body, which is given by:
N = m * g
where g is the acceleration due to gravity (g = 10 m/s²).
Substituting the normal force into the friction equation, we have:
f = μ * (m * g)
Since the net force is zero, the force of friction is equal to the applied force of 20 N:
f = 20 N
Therefore, we can set up the equation:
20 N = μ * (40 kg * 10 m/s²)
Simplifying, we get:
20 N = μ * 400 kg*m/s²
Dividing both sides by 400 kg*m/s², we find:
μ = 20 N / 400 kg*m/s²
μ = 0.05