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 209.8 kg. If the horse moves the sled at a constant speed of 1.730 m/s, what is the power needed to accomplish this?
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To calculate the power needed to move the sled at a constant speed, we can use the formula:
Power = Force x Velocity
First, let's calculate the force required to overcome the friction. The frictional force can be found using the equation:
Frictional force = 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 gravity
Here, the mass of the sled, including the load, is given as 209.8 kg. We can assume that the acceleration due to gravity is 9.8 m/s^2.
Weight = 209.8 kg x 9.8 m/s^2 = 2052.04 N
Now, we can calculate the frictional force:
Frictional force = 0.195 x 2052.04 N = 399.642 N
Since the sled is moving at a constant speed, the force applied by the horse must be equal in magnitude and opposite in direction to the frictional force. So, the force applied by the horse is also 399.642 N.
Finally, we can calculate the power:
Power = Force x Velocity = 399.642 N x 1.73 m/s = 691.97 watts
Therefore, the power needed to move the sled at a constant speed of 1.73 m/s is 691.97 watts.
To calculate the power needed to move the sled at a constant speed, we need to consider the forces acting on the sled.
First, let's find the force of friction using the formula: f = μN, where μ is the coefficient of friction and N is the normal force.
The normal force is equal to the weight of the sled, which can be calculated using the formula: N = mg, where m is the mass of the sled (including the load) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now we can calculate the force of friction: f = 0.195 * (209.8 kg * 9.8 m/s^2).
Next, we need to find the work done to overcome the force of friction. The work done is equal to the product of the force and the distance traveled by the sled. In this case, the distance traveled is not given, but since the speed is constant, we can assume that the force of friction is balanced by the force applied by the horse.
Therefore, the work done to overcome the force of friction is zero.
Finally, we can calculate the power needed to accomplish this. Power is the rate at which work is done, which is equal to the work done divided by the time taken. Since the work done is zero, the power needed to move the sled at a constant speed of 1.730 m/s is also zero.
In conclusion, the power needed to accomplish this is zero.