A sled is pulled with a horizontal force of 17 N along a level trail, and the acceleration is found to be 0.40 m/s2. An extra mass m = 4.4 kg is placed on the sled. If the same force is just barely able to keep the sled moving, what is the coefficient of kinetic friction between the sled and the trail?
Let the friction force be f without the added mass. It increases to
f (M+4.4)/M with the added mass.
You have two unknowns (f and M) and need two equations.
17 - f = M*a = M*0.40
17 - f*(M+4.4)/M = (M+4.4)*0 = 0 (zero acceleration with added mass)
f*(M+4.4)/M -Ff = 0.4 M
f*4.4/M = 0.4M
f = M^2/11
17-f = 17 - M^2/11 = 0.4M
Solve for M and use that to solve for f. Take the postitive root when solving for M.
The coefficient of kinetic friction is
muk = f/(M*g)
That makes a lot more sense now. Thanks!
To find the coefficient of kinetic friction, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Here's how we can find the coefficient of kinetic friction:
1. Calculate the net force acting on the sled:
Force (F) = mass (m) × acceleration (a)
Given: m = 4.4 kg, a = 0.40 m/s²
Therefore, F = 4.4 kg × 0.40 m/s² = 1.76 N
2. Subtract the force applied to the sled from the net force to find the force of friction:
Force of friction (Ff) = net force (F) - applied force
Given: applied force = 17 N
Therefore, Ff = 1.76 N - 17 N = -15.24 N (Note: The negative sign indicates that the force of friction acts opposite to the applied force.)
3. Calculate the coefficient of kinetic friction:
The coefficient of kinetic friction (μk) is defined as the ratio of the force of friction to the normal force between the surfaces involved.
We know that the normal force acting on an object on a level surface is equal to the weight of the object:
Normal force (N) = weight (mg)
Given: m = 4.4 kg
Therefore, N = 4.4 kg × 9.8 m/s² (acceleration due to gravity) = 43.12 N
Now, we can find the coefficient of kinetic friction:
μk = Ff / N
μk = -15.24 N / 43.12 N ≈ -0.353 (Note: The negative sign is ignored in this calculation.)
Hence, the coefficient of kinetic friction between the sled and the trail is approximately 0.353.
Note: The negative sign indicates that the force of friction is acting opposite to the applied force. However, in this case, it is ignored because the coefficient of kinetic friction is a positive quantity.