Final answer:
Yes. The mule can accelerate the cart as long as the force it exerts exceeds the frictional force. Newton's third law applies to forces on different objects and thus does not prevent acceleration. The work done by the mule can be computed using the force exerted, distance, and the angle at which the force is applied.
Step-by-step explanation:
Yes, it is possible for the mule to accelerate the cart, despite the force pulling back on the mule being equal in size to the force the mule exerts on the cart due to Newton's third law. This is because these forces are acting on different objects. The mule's force is on the cart, while the cart's force is on the mule. What is essential for acceleration is that there is a net force acting on the cart.
If the mule exerts a force greater than the opposing frictional force of the cart, the cart will accelerate forward in the direction of the net force. Consider a case from history, when mules pulled barges along canals. The work done by the mule can be calculated considering the force exerted, the distance traveled, and the angle of application.
Using the provided information, the mule exerts a 1200 N force at a 20-degree angle for 10 km (10,000 meters). The work done by the mule on the barge, W, can be calculated using the formula W = F × d × cos(\theta), where F is the force exerted, d is the distance traveled, and \theta is the angle between the force and the direction of travel. Hence, the work done will only consider the component of the force that is in the direction of the movement (the horizontal component).
First, calculate the horizontal component of the force:
F_horizontal = 1200 N × cos(20°)
Then, use this component to find out the work:
W = F_horizontal × 10,000 m
It is important to note that the mule must overcome force of friction to get the cart moving. Once moving, if the force the mule applies equals the frictional force, the cart will move at a constant velocity according to Newton's first law.