A horse draws a sled horizontally across a snow-covered field. The coefficient of friction between the sled and the snow is 0.195, and the mass of the sled, including the load, is 202.4 kg. If the horse moves the sled at a constant speed of 1.857 m/s, what is the power needed to accomplish this?
To calculate the power needed to accomplish this task, we need to use the formula:
Power = Force × Velocity
In this case, the force we need to calculate is the force of friction between the sled and the snow. The force of friction can be determined using the equation:
Force of friction = coefficient of friction × normal force
To find the normal force, we need to consider that the sled is moving horizontally, and therefore, there is no vertical acceleration. The normal force (N) is equal to the weight of the sled (mg), where g is the acceleration due to gravity (9.8 m/s²).
So, the normal force is:
N = mg
Now, let's substitute this value into the equation for the force of friction:
Force of friction = coefficient of friction × mg
Since the sled is moving at a constant speed, the force of friction is equal to the force applied by the horse to overcome it:
Force of friction = Force applied by the horse
Now we can calculate the power:
Power = Force applied by the horse × velocity
Substituting the equation for force of friction into the power equation:
Power = (coefficient of friction × mg) × velocity
Now, let's plug in the given values:
coefficient of friction (μ) = 0.195
mass of sled (m) = 202.4 kg
velocity (v) = 1.857 m/s
acceleration due to gravity (g) = 9.8 m/s²
Calculating:
Power = (0.195 × 202.4 kg × 9.8 m/s²) × 1.857 m/s
Simplifying:
Power = 369.1056 Joules/second or 369.1 Watts
Therefore, the power needed to accomplish this task is approximately 369.1 Watts.
P=W/t = F(fr)•s/t=F(fr) •v =
=μ•m•g•v =0.195•202.4•9.8•1.857 = …