Question

Question 5 - Suppose you are sitting on a platform that is subject to very small friction forces - for example, a large frictionless puck on a huge air table or a boat floating on water. You are initially at rest and you have no paddles and no way of pushing yourself along the surface, but you wish to accelerate yourself and your platform to a finite velocity is some particular direction. You have with you a basket of rocks. A. What might you do to accelerate yourself in the direction you wish? What might you do if you wish to slow down or stop? Analyze this situation carefully, drawing well-separated free-body diagrams for a rock, yourself, and the platform. Explain, in terms of Newton's laws, what is happening to make your transportation possible. B. In light of the thinking you have done in part A, analyze, with appropriate free-body diagrams, what must be happening (1) when you paddle a boat through water; (2) when a propeller accelerates a boat or an airplane. C. Why is the action of the propeller still necessary once the boat or plane has been accelerated to the desired velocity? D. Why is a propeller useless on a spaceship?

Answer 1

A.

To accelerate oneself in some desired direction, the rocks must be pushed of flung with a significant amount of force in the opposite direction.

To decelerate or stop, the rocks must be pushed or flung in the direction of motion.

The separate FBD's

OFR C Fs FRE

FR is the force in the rocks

FS is the force on the person on the platform

FP is the force on the platform

Here f is the small frictional force and ignoring gravity

FBD of the entire system

FE afp FR FR Z f

Newton's third law makes transportation possible. Since the rocks are held by the person who is sitting on the platform, the entire system is a single entitiy, and all the forces acting on the system should sum up to 0. It is the same reason why one cannot lift up a chair they are sitting on. The rocks flung back with some force must be balanced by forces on the person and the platform they are sitting on(by the rocks). Since the force of friction is small, the platform can slide.

B.

1.&2.

In both cases, the paddles/propeller apply a force on water or air which serves as the medium in which the boat/airplane is suspended. When the fluid is pushed back, the fluid in turn pushes back on the boat/airplane, thus it moves.

G 아

Left:paddle

Right:propeller

C.

The propeller is still necessary to maintain a certain velocity. Air and water are resistive media with significant friction. The frictional force resists the motion of the object in it and slows it down. If the propeller is turned off, after some time the boat/airplane will come to rest.

D.

Propellers are useless in space since it is vacuum. There is no medium to push against that will create propulsion. Also, since it is a vacuum, spaceships do not slow down, until they encounter the atmosphere of a planet or an actual material surface like the surface of the moon.