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
To find the work done by the dogs, we can use the formula:
Work = Force * Distance * cos(θ)
Where:
- Force is the force applied by the dogs to drag the sled.
- Distance is the distance traveled by the sled.
- θ is the angle between the force applied and the direction of motion. Since the sled is being dragged horizontally, the angle is 0 degrees, and cos(0) = 1.
First, let's find the force applied by the dogs. The force can be calculated using the following formula:
Force = Frictional Force
The frictional force can be calculated using the formula:
Frictional Force = μ * Normal Force
Where:
- μ is the coefficient of friction.
- Normal Force is the force exerted by the surface on the sled in the vertical direction. In this case, the sled is on a horizontal surface, so the Normal Force is equal to the weight of the sled.
Weight = mass * acceleration due to gravity
So, the weight of the sled is:
Weight = 119 kg * 9.8 m/s^2
Now, we can calculate the frictional force:
Frictional Force = 0.172 * Weight
Next, we can plug in the values into the first formula to find the work done:
Work = Force * Distance * cos(θ)
Work = Frictional Force * Distance * cos(θ)
Work = (0.172 * Weight) * 2.1 km * cos(0)
Finally, we need to convert the distance from kilometers to meters and the answer from joules to kilojoules:
Work = (0.172 * Weight) * (2.1 km * 1000 m/km) * 1 J/1000 kJ
Now, you can substitute the values to calculate the work done by the dogs.