Tell all A sled starts at the top of the hill shown in Figure P3.87. Add any information that yo

Tell all A sled starts at the top of the hill shown in...

Key Concepts

Motion on an Inclined Plane

Motion on an inclined plane involves analyzing the components of gravitational force acting parallel and perpendicular to the slope. This breakdown is essential to determine the net force causing the sled's acceleration downward, as well as the normal force, which influences frictional forces acting against the motion.

Newton's Laws of Motion

Newton's Laws provide the foundation for understanding the motion of any object. In this context, they explain how forces like gravity, friction, and normal force interact to produce acceleration when the sled starts moving down the hill, and deceleration as it comes to a stop. These laws help predict the changes in velocity and direction during the motion.

Energy Transformation

This concept describes the conversion of energy from one form to another. For a sled on a hill, gravitational potential energy at the top is transformed into kinetic energy as the sled accelerates down the slope. As the sled moves, energy conversions also take place from kinetic energy into heat due to dissipative forces.

Friction and Dissipative Forces

Friction is a resistive force that opposes motion and plays a crucial role in converting mechanical energy into heat energy. In the scenario of a sled descending an incline, friction—arising from interaction with the surface and air resistance—eventually dissipates the sled's kinetic energy, causing it to slow down and stop.

Work-Energy Principle

The work-energy principle connects the work done by all forces (including nonconservative forces like friction) to the change in energy of the system. It provides a framework to analyze how the work done by gravity increases kinetic energy and how the negative work done by friction reduces it, eventually bringing the sled to a stop.

Transcript

00:01 Question 87.

00:03 Tell all a sled starts at the top of a hill and okay, let's just draw exactly what's going on here.

00:12 And we'll mark the position of some sort of sled while it's halfway down the hill.

00:19 Basically, it says add any information that you think is reasonable about of the process that ensues when the sled goes down the hill and finally stops.

00:27 And tell us everything you can about this process.

00:31 Well, reasonable information.

00:34 Would be things like the coefficient of friction.

00:37 We'll mark on first the force diagrams.

00:41 We have a normal force, umg, which is our weight, and of course a frictional force opposing our sliding motion, so the force of friction here.

00:51 It very much matters what angle the hill is at, so theta would be appropriate also to note, leading us to a second ability to draw theta as this angle here.

01:07 All the key information would be things like the coefficient of friction.

01:12 This could be something like 0 .1, especially if it was a ski slope.

01:17 We're not having a high amount of friction on that sort of slope.

01:22 This would be a coefficient of kinetic friction.

01:27 So information we could work out, for example, well, assuming this here, we've got a distance of the slide of d, and therefore let's work out.

01:37 For example how you could work out the acceleration and the acceleration is going to come about through the net force parallel to the slope which is going to be the component of weight parallel to the slope mg sine theta taken just from evaluating the downwards motion according to weight and resisted by the friction or force which would mean that we'd have to subtract off the coefficient of kinetic friction multiplied by the normal force but the normal force is fairly well known to is at this stage it's mg cosine theta because of course the perpendicular component of weight will balance out with the normal force and this is going to equal our m a and very quickly we can work out that mass counters on both sides leaving g multiplied by in parentheses sine theta minus m u k cosine theta is equal to acceleration.

02:40 Lovely.

02:42 So what would our velocity be at the bottom of the slope? well, our final velocity would equal our initial velocity plus 2a .s, and we'll assume for the beginning that our initial velocity is zero.

03:00 We start from rest...

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