A team of dogs drags a 119 kg sled 2.1 km over
a horizontal surface at a constant speed. The
coefficient of friction between the sled and the
snow is 0.172.
The acceleration of gravity is 9.8 m/s
2
.
Find the work done by the dogs.
Answer in units of kJ
W=W(fr)= μ•m•g•s
Why did the dog team join the circus? Because they wanted to show off their impressive work in dragging a 119 kg sled! To find the work done by the dogs, we can use the formula:
Work = force * distance * cos(theta)
Now, let's break down the problem: the force exerted by the dogs is the force of friction acting against them. The equation for friction is given by:
Friction = coefficient of friction * normal force
Since the sled is being pulled horizontally, the normal force is equal to the sled's weight:
Normal force = mass * gravity
Combining these equations, we have:
Friction = coefficient of friction * mass * gravity
Now, we can calculate the frictional force. Using the given values, we find:
Friction = 0.172 * 119 kg * 9.8 m/s^2
Next, we multiply the frictional force by the distance traveled to find the total work done:
Work = Friction * distance
Work = (0.172 * 119 kg * 9.8 m/s^2) * 2.1 km
Finally, let's convert the units from joules to kilojoules:
Work = (0.172 * 119 kg * 9.8 m/s^2 * 2.1 km) / 1000
So, the work done by the dogs is approximately equal to: *calculates* *counts fingers* *grabs calculator* *drum roll* 43.25 kJ.
Looks like those dogs really put their muscles to work!
To find the work done by the dogs, we need to calculate the force required to pull the sled and then multiply it by the distance traveled.
First, let's calculate the force required to overcome friction. The formula for friction force is:
Friction force = coefficient of friction × normal force
The normal force can be calculated by multiplying the mass of the sled by the acceleration due to gravity:
Normal force = mass × acceleration due to gravity
Normal force = 119 kg × 9.8 m/s^2
Next, substitute the given coefficient of friction into the formula:
Friction force = 0.172 × (mass × acceleration due to gravity)
Now, let's calculate the force required to pull the sled. Since the sled is moving at a constant speed, the net force on the sled is zero. This means the force of friction must be equal to the force applied by the dogs:
Force applied by the dogs = Friction force
Now, we can calculate the work done by the dogs. The formula for work is:
Work = Force × distance
Work = (Force applied by the dogs) × distance traveled
Finally, substitute the values into the formula and solve for work:
Work = (Force applied by the dogs) × 2.1 km
To convert the distance from kilometers to meters, multiply by 1000:
Work = (Force applied by the dogs) × 2.1 km × 1000 m/km
The final answer will be in joules (J), but the question asks for the answer in kilojoules (kJ). To convert joules to kilojoules, divide by 1000:
Work = [(Force applied by the dogs) × 2.1 km × 1000 m/km] / 1000
Simplify and calculate the answer to find the work done by the dogs in kilojoules.