A 125-kg sled is dragged by a team of dogs a distance of 2 km over a horizontal surface at a constant velocity. If the coefficient of friction between the sled and the snow is 0.15, find (a) the work done by the team of dogs and (b) the energy lost due to friction
To find the work done by the team of dogs, we can use the formula:
Work = force x distance
In this case, the force acting against the motion of the sled is the force of friction. The work done by the team of dogs is equal to the work done to overcome the force of friction.
Since the sled is moving at a constant velocity, the net force acting on the sled is zero. This means that the force of friction must be equal in magnitude and opposite in direction to the force applied by the dogs.
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction x normal force
The normal force is equal to the weight of the sled, which can be calculated using the formula:
Weight = mass x acceleration due to gravity
Given:
Mass of the sled (m) = 125 kg
Coefficient of friction (μ) = 0.15
Acceleration due to gravity (g) = 9.8 m/s²
Let's calculate the normal force and the force of friction:
Weight = mass x acceleration due to gravity
Weight = 125 kg x 9.8 m/s²
Weight = 1225 N
Force of friction = coefficient of friction x normal force
Force of friction = 0.15 x 1225 N
Force of friction = 183.75 N
Now, let's calculate the work done:
Work = force x distance
Work = force of friction x distance
Work = 183.75 N x 2000 m
Work = 367,500 J (Joules)
Therefore, the work done by the team of dogs is 367,500 Joules.
To find the energy lost due to friction, we use the work-energy principle. According to this principle, the work done against friction is equal to the energy lost due to friction.
So, the energy lost due to friction is also equal to 367,500 Joules.
To find the work done by the team of dogs, we can use the formula:
Work = Force x Distance x cos(θ)
Where:
Force = μmg (μ: coefficient of friction, m: mass, g: acceleration due to gravity)
Distance = 2 km
θ = angle between the force and the direction of motion (θ = 0 degrees for horizontal motion)
Let's calculate each part step by step:
(a) Work done by the team of dogs:
First, calculate the force exerted by the team of dogs:
Force = μmg
Plugging in the values:
Force = 0.15 x 125 kg x 9.8 m/s^2
Force = 183.75 N (rounded to two decimal places)
Now, calculate the work done:
Work = Force x Distance x cos(θ)
Work = 183.75 N x 2000 m x cos(0 degrees)
Work = 367,500 J (rounded to two decimal places)
Therefore, the work done by the team of dogs is 367,500 Joules.
(b) Energy lost due to friction:
The energy lost due to friction is equal to the work done against friction. Since the velocity is constant and there is no change in kinetic energy, the work done against friction is equal to the energy lost.
Energy lost due to friction = Work done against friction
To calculate the work done against friction, we can use the formula:
Work against friction = Force x Distance
Plugging in the values:
Work against friction = 183.75 N x 2000 m
Work against friction = 367,500 J (rounded to two decimal places)
Therefore, the energy lost due to friction is 367,500 Joules.
a.
W=μmgs=0.15•125•9.8•2000=
b.
E=-W