A team of dogs drags a 112 jk sled 2.23 km over a horizontal surface at a constant speed. The coefficient of friction between the sled and the snow is 0.181. The acceleration of gravity is 9.8 m/s. Find the work done by the dogs
Well, it seems like those dogs really had a "ruff" time pulling that sled! Let's calculate the work done by these hardworking canines.
The work done can be calculated using the formula:
Work = Force × Distance × Cosine(theta)
First, let's find the force applied by the dogs to overcome the friction. We can do this by multiplying the coefficient of friction by the normal force. The normal force is the force exerted by the sled on the dogs, which is equal in magnitude and opposite in direction to the force of gravity acting on the sled.
Normal force = mass × gravity
Given that the sled weighs 112 jk, we have:
Normal force = 112 jk × 9.8 m/s²
Now, let's find the force of friction:
Force of friction = coefficient of friction × normal force
Finally, we can find the work done by multiplying the force of friction by the distance the sled is dragged:
Work = Force of friction × Distance × Cosine(theta)
Since the sled is pulled horizontally, theta is the angle between the force of friction and the displacement, and therefore it is 0 degrees.
Now let's plug in the values and calculate the work done!
To find the work done by the dogs in pulling the sled, we can use the equation:
Work = Force * Distance
First, let's calculate the force the dogs need to exert to overcome the friction between the sled and the snow. The frictional force can be calculated using the equation:
Frictional force = coefficient of friction * normal force
The normal force acting on the sled is equal to the weight of the sled, which can be calculated using the equation:
Weight = mass * gravity
Given that the sled has a mass of 112 kg and the acceleration due to gravity is 9.8 m/s^2, we can substitute the values into the equation to find the weight:
Weight = 112 kg * 9.8 m/s^2 = 1097.6 N
Now, we can calculate the frictional force:
Frictional force = 0.181 * 1097.6 N = 198.6776 N (rounded to 4 decimal places)
Since the sled is being pulled at a constant speed, the force exerted by the dogs must be equal to the frictional force:
Force = Frictional force = 198.6776 N
Next, let's calculate the distance the dogs pulled the sled. Given that the distance is 2.23 km, we need to convert it to meters:
Distance = 2.23 km * 1000 m/km = 2230 m
Now, we have all the values needed to calculate the work done by the dogs:
Work = Force * Distance = 198.6776 N * 2230 m = 443221.84 J (rounded to 2 decimal places)
Therefore, the work done by the dogs to pull the sled is approximately 443,221.84 Joules.
To find the work done by the dogs, we first need to calculate the force required to overcome the friction between the sled and the snow. The work done can be calculated using the formula:
Work = Force * Distance
The force can be determined using Newton's second law, which states that Force = Mass * Acceleration. Rearranging the equation, we have:
Force = Mass * Acceleration
To find the mass of the sled, we can use the formula:
Mass = Weight / Acceleration due to gravity
The weight is given by:
Weight = Mass * Acceleration due to gravity
Substituting this equation into the equation for force, we have:
Force = (Mass * Acceleration due to gravity) * Acceleration
Now, we have the force required to overcome friction. The frictional force can be calculated using the formula:
Frictional Force = Coefficient of friction * Normal force
The normal force can be determined using the equation:
Normal force = Weight
Substituting this into the equation for friction, we have:
Frictional Force = Coefficient of friction * Weight
We can now calculate the work done using the formula introduced earlier:
Work = Frictional Force * Distance
Substituting the equation for frictional force, we have:
Work = (Coefficient of friction * Weight) * Distance
Plugging in the given values, we have:
Work = (0.181 * Weight) * 2.23 km
Note: We need to convert the distance from kilometers to meters. 1 km = 1000 m.
Now, we have the equation for work, and we can proceed with the calculation.