A team of dogs drags a 150 kg sled 1.39 km
over a horizontal surface at a constant speed. The coefficient of friction between the sled and the snow is 0.236.
The acceleration of gravity is 9.8 m/s^2.
Find the work done by the dogs.
Also,
What is the energy lost due to friction?
The unit should be in kJ
Well, let's start by finding the work done by the dogs.
The work done is given by the formula:
Work = Force x Distance
To find the force, we need to consider the forces acting on the sled. The only horizontal force is the force of friction, which can be calculated as:
Friction = coefficient of friction x Normal force
The normal force is equal to the weight of the sled, which can be calculated as:
Weight = mass x acceleration due to gravity
So, Weight = 150 kg x 9.8 m/s^2 = 1470 N
Now, let's calculate the frictional force:
Friction = 0.236 x 1470 N = 346.92 N
Since the sled is moving at a constant speed, the force applied by the dogs is equal in magnitude but opposite in direction to the force of friction. Hence, the work done by the dogs can be calculated as:
Work = Force x Distance = Friction x Distance
Given that the distance is 1.39 km = (1.39 x 1000 m), we can calculate the work done by the dogs:
Work = 346.92 N x 1.39 x 1000 m = 482,716 J
Now, let's find the energy lost due to friction.
Energy lost due to friction is equal to the work done against friction. Since we already found the work done by the dogs, which is equal to the work done against friction, the energy lost due to friction is simply:
Energy lost = Work = 482,716 J
To convert this into kilojoules (kJ):
Energy lost = 482,716 J * (1 kJ / 1000 J) = 482.716 kJ
So, the energy lost due to friction is approximately 482.716 kJ.
I hope that answers your question, while giving you a little bit of a workout for your brain!
To find the work done by the dogs, we need to calculate the force acting on the sled and multiply it by the distance traveled.
1. Calculate the force of friction:
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * Normal force
Normal force = mass * gravity
Normal force = 150 kg * 9.8 m/s^2
Force of friction = 0.236 * (150 kg * 9.8 m/s^2)
2. Calculate the work done:
Work = force * distance
Work = (Force of friction) * (1.39 km)
Note that we need to convert 1.39 km to meters first.
1.39 km = 1.39 * 1000 m = 1390 m
Work = (Force of friction) * 1390 m
3. Convert the work to kilojoules (kJ):
Since 1 Joule (J) = 1 Newton (N) * 1 meter (m),
1 kJ = 1000 J
Work in kJ = (Work in Joules) / 1000
Now let's calculate the work done by the dogs and the energy loss due to friction.
Calculation:
Normal force = 150 kg * 9.8 m/s^2 = 1470 N
Force of friction = 0.236 * 1470 N = 346.92 N
Work = 346.92 N * 1390 m = 482,258.8 J
Work in kJ = 482,258.8 J / 1000 = 482.26 kJ
The work done by the dogs is 482.26 kJ.
To find the energy lost due to friction, we need to consider that work is done both by the dogs (positive work) and against friction (negative work). Hence, the energy lost due to friction is the negative of the work done by the dogs.
Energy lost kJ = -482.26 kJ
Therefore, the energy lost due to friction is 482.26 kJ.
To find the work done by the dogs, we can use the formula:
Work = Force x Distance
The force acting on the sled is the force of friction between the sled and the snow. The frictional force can be calculated using the formula:
Force of Friction = coefficient of friction x Normal Force
The normal force is the force exerted by the surface on the object perpendicular to the surface. In this case, as the sled is on a horizontal surface, the normal force is equal to the weight of the sled.
Normal Force = Mass x Gravity
Now, let's calculate the normal force:
Mass of the sled = 150 kg
Gravity = 9.8 m/s^2
Normal Force = 150 kg x 9.8 m/s^2 = 1470 N
Next, we can calculate the force of friction:
Coefficient of Friction = 0.236
Force of Friction = 0.236 x 1470 N = 346.92 N
Now that we have the force of friction, let's calculate the work done by the dogs:
Distance = 1.39 km = 1390 m
Work = Force x Distance
Work = 346.92 N x 1390 m
Finally, let's convert the work to kilojoules (kJ):
1 J = 0.001 kJ
Work (kJ) = (Work (J)) x 0.001
Substitute the values:
Work (kJ) = (346.92 N x 1390 m) x 0.001
Now, calculate the value to find the work done by the dogs.
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To find the energy lost due to friction, we can use the concept of work. The energy lost due to friction is equal to the work done against friction.
Energy Lost = Work against Friction
Since we have already calculated the work done by the dogs, we can use that value to find the energy lost due to friction. Therefore, the energy lost due to friction is equal to the work done by the dogs.
So, the energy lost due to friction is the same as the work done by the dogs, and its value has already been calculated.