a 17 kg sled is being pulled along the horizontal snow covered ground by a horizontal force of 22 N. starting from rest the sled attains a speed of 1.9 m/s in 7.8 m find the coefficient of kinetic fiction between the runners of the sled and the snow.
To find the coefficient of kinetic friction between the runners of the sled and the snow, we can use Newton's second law of motion.
The equation we will be using is:
Fnet = m * a
Where:
Fnet is the net force acting on the sled,
m is the mass of the sled, and
a is the acceleration of the sled.
First, let's calculate the net force acting on the sled. In this case, the only horizontal force acting on the sled is the pulling force of 22 N. So, the net force is also 22 N.
Now, let's find the acceleration of the sled. We can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v is the final velocity (1.9 m/s),
u is the initial velocity (0 m/s, since the sled starts from rest),
a is the acceleration (which we want to find), and
s is the displacement (7.8 m).
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
= (1.9^2 - 0^2) / (2 * 7.8)
= 3.61 / 15.6
= 0.231 m/s^2
Now, substitute the values into the equation Fnet = m * a:
22 N = 17 kg * 0.231 m/s^2
Solving for the coefficient of kinetic friction:
Fnet = μ * N
Since the sled is on a horizontal surface, the normal force (N) is equal to the weight (mg). Therefore, N = 17 kg * 9.8 m/s^2 = 166.6 N.
Substituting the values, we can solve for μ:
22 N = μ * 166.6 N
μ = 22 N / 166.6 N
≈ 0.132
So, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.132.
a=v²/2s =1.9²/2•7.8=0.23 m/s²
ma=F(fr)=μN=μmg
μ=a/g = 0.23/9.8=0.23