Three huskies are pulling a dog sled. The mass of the driver, sled and supplies is 145 kg. Snowy is pulling with a force of 83 N and 15.5degrees to the left of forward. Buster is pulling with a force of 75 N at 9degrees right of forward and Prince is pulling with a force of 77N at 12 degrees right of forward. The sled is moving forward at a constant velocity. What is the coefficient of kinetic friction between the sled and the snow?
Any help with this questions, would be greatly appreciated. Thanks!
Ws = mg = 145kg * 9.8N/kg = 1421 N. = Wt of sled incl. load.
Forward = 0 Deg.
Fs = 1421N @ 0 Deg. =Force of sled incl. load.
Fp=1421*sin(0)=0=Force parallel to gnd.
Fv = 1421*cos(0) = 1421 N. = Force perpendicular to gnd.
F1 = 83N @ 15.5 Deg.,CCW.
F2 = 75N @ 351 Deg.,CCW.
F3 = 77N @ 348 Deg.,CCW.
X=hor.=83*cos15.5+75*cos351+77*cos348=
229.4 N.
Y = 83*sin15.5+75*sin351+77*sin348=-5.56 N.
tanA = Y/X=(-5.56) / 229.4 = =0.024237
A = -1.39 Deg.,CW. = -1.39 + 369=358.6
Deg.,CCW.
Fap = X/cosA = 229.4 / cos358.6 = 229.5 N. @ 358.6 Deg. = Force applied.
Fn = Fap - Fp -Fk = ma = 0. a = 0.
229.5*cos358.6 - 0 - 1421u = 0.
1421u = 229.5*cos358.6 = 229.43.
u = 229.43 / 1421 = 0.161 = Coefficient of kinetic friction.
Thank you so much for your help! But just one question what does CCW mean? And once again, I appreciate your help immensly!
To find the coefficient of kinetic friction between the sled and the snow, we first need to determine the net force acting on the sled.
The forces pulling the sled are Snowy, Buster, and Prince. We can break down each force into its x and y components.
For Snowy:
Force Snowy (x) = 83 N * cos(15.5°)
Force Snowy (y) = 83 N * sin(15.5°)
For Buster:
Force Buster (x) = 75 N * cos(-9°) [note: Since it is "right of forward", we use a negative angle]
Force Buster (y) = 75 N * sin(-9°)
For Prince:
Force Prince (x) = 77 N * cos(-12°) [note: Since it is "right of forward", we use a negative angle]
Force Prince (y) = 77 N * sin(-12°)
The net force acting on the sled can be calculated by summing up the forces in both the x and y directions:
Net force (x) = Force Snowy (x) + Force Buster (x) + Force Prince (x)
Net force (y) = Force Snowy (y) + Force Buster (y) + Force Prince (y)
Since the sled is moving at a constant velocity, the net force in the x-direction (horizontal) is zero:
Net force (x) = 0
Therefore, we can set up the equation:
Force Snowy (x) + Force Buster (x) + Force Prince (x) = 0
Plugging in the values:
83 N * cos(15.5°) + 75 N * cos(-9°) + 77 N * cos(-12°) = 0
Solving this equation gives us the sum of the x-components of the forces.
Now we can find the net force in the y-direction (vertical):
Net force (y) = Force Snowy (y) + Force Buster (y) + Force Prince (y)
Plugging in the values:
83 N * sin(15.5°) + 75 N * sin(-9°) + 77 N * sin(-12°)
Solving this equation gives us the sum of the y-components of the forces.
Since the sled is moving at a constant velocity, the net force in the y-direction (vertical) must be balanced by the force of kinetic friction:
Net force (y) = Kinetic friction
We can now calculate the coefficient of kinetic friction using the formula:
Coefficient of kinetic friction = Kinetic friction / (mass of the sled * acceleration due to gravity)
Substituting the values, we get:
Coefficient of kinetic friction = (Net force (y)) / (mass of the sled * acceleration due to gravity)
Calculate the final value using the given information and the above steps, and you will have the coefficient of kinetic friction between the sled and the snow.
To find the coefficient of kinetic friction between the sled and the snow, we can use Newton's second law of motion, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's break down the forces acting on the sled. Snowy is pulling with a force of 83 N to the left of forward, Buster is pulling with a force of 75 N at 9 degrees right of forward, and Prince is pulling with a force of 77 N at 12 degrees right of forward.
To simplify the analysis, let's resolve these forces into their horizontal and vertical components. Since the sled is moving forward at a constant velocity, we know that the net force acting on it in the horizontal direction must be zero. This means that the horizontal components of the forces must cancel each other out.
Let's calculate the horizontal component of the force for each dog:
For Snowy:
Horizontal component = Force * cos(angle)
Horizontal component = 83 N * cos(15.5 degrees)
For Buster:
Horizontal component = Force * cos(angle)
Horizontal component = 75 N * cos(9 degrees)
For Prince:
Horizontal component = Force * cos(angle)
Horizontal component = 77 N * cos(12 degrees)
Next, let's calculate the net horizontal force on the sled by summing up the horizontal components of the forces exerted by each dog:
Net horizontal force = Sum of horizontal components of forces
Now that we have the net horizontal force acting on the sled, we can use it to calculate the coefficient of kinetic friction between the sled and the snow. The coefficient of kinetic friction (μ) is defined as the ratio of the force of friction (Ffriction) to the normal force (Fnormal) between the two surfaces:
μ = Ffriction / Fnormal
Since the sled is moving at a constant velocity, the net horizontal force is equal to the force of friction:
Net horizontal force = Ffriction
Finally, we can substitute the value of the net horizontal force into the equation to solve for the coefficient of kinetic friction:
μ = Net horizontal force / Fnormal
For the sake of completing this answer, let's assume that the force of friction is acting in the opposite direction of the net horizontal force.
Unfortunately, we don't have the value for the net horizontal force or the normal force in the question. Without these values, it is not possible to calculate the coefficient of kinetic friction between the sled and the snow.