Q1. Assume that a horse pulls a sleigh in a way that the sleigh moves at constant velocity. What is the work being done on the sleigh (a) by the horse, (b) by the Earth, and (c) by the force of friction? Determine whether the work is positive, zero, or negative.
(a) The work being done on the sleigh by the horse is positive. It's like a horse lifting weights at the gym, except the "weights" in this case are the sleigh. So the horse is doing positive work on the sleigh.
(b) The work being done on the sleigh by the Earth is zero. The Earth isn't actively doing any work on the sleigh in this situation. It's just providing a surface for the sleigh to move on.
(c) The work being done on the sleigh by the force of friction is negative. Friction acts opposite to the direction of motion, so as the horse pulls the sleigh forward, the force of friction opposes that motion and does negative work on the sleigh.
In summary:
(a) positive work by the horse,
(b) zero work by the Earth,
(c) negative work by the force of friction.
(a) The work being done on the sleigh by the horse can be determined by the equation:
Work = Force × Distance × cos(θ)
In this case, since the sleigh is moving at a constant velocity, its acceleration is zero. Therefore, the net force acting on the sleigh must also be zero.
The force applied by the horse must be equal and opposite to the force of friction acting on the sleigh, so the work done by the horse is zero.
(b) The work being done on the sleigh by the Earth can be calculated using the same equation:
Work = Force × Distance × cos(θ)
Since the sleigh is moving at a constant velocity, the force exerted by the Earth to move the sleigh is equal and opposite to the force of friction. Therefore, the work done by the Earth is zero.
(c) The work being done on the sleigh by the force of friction can also be determined using the equation:
Work = Force × Distance × cos(θ)
In this case, the force of friction is in the opposite direction to the motion of the sleigh. Hence, the angle between the direction of motion and the force of friction is 180 degrees. Therefore, the cosine of 180 degrees is -1.
Since the work equation involves the cosine of the angle between the force and the displacement, and the cosine of 180 degrees is -1, the work done by the force of friction is negative.
In summary:
(a) The work done by the horse is zero.
(b) The work done by the Earth is zero.
(c) The work done by the force of friction is negative.
To determine the work being done on the sleigh by different forces, we can use the formula for work:
Work = Force * Distance * cos(theta),
where "Force" is the applied force, "Distance" is the displacement caused by the force, and "theta" is the angle between the direction of the force and the direction of displacement.
(a) Work done on the sleigh by the horse:
Since the sleigh moves at constant velocity, there is no acceleration, which means the net force acting on the sleigh is zero. Therefore, the work done on the sleigh by the horse is zero.
(b) Work done on the sleigh by the Earth:
The Earth's gravitational force acts vertically downwards, while the displacement of the sleigh is horizontal. Therefore, the angle between the two is 90 degrees, and cos(90) is zero. This implies that no work is done on the sleigh by the Earth.
(c) Work done on the sleigh by the force of friction:
The sleigh moves at constant velocity, which indicates that the net force acting on it is zero. Hence, the force of friction must balance the force applied by the horse. Since the displacement is in the same direction as the force of friction, the angle between them is zero degrees, and cos(0) is one. Thus, the work done on the sleigh by the force of friction is positive.
In summary:
(a) Work done on the sleigh by the horse is zero.
(b) Work done on the sleigh by the Earth is zero.
(c) Work done on the sleigh by the force of friction is positive.