A 1500 kg car is approaching the hill shown in Figure P 10.39 at 10 m / s when it suddenly runs

A 1500 kg car is approaching the hill shown in Figure P...

A $1500 \mathrm{kg}$ car is approaching the hill shown in Figure $\mathrm{P} 10.39$ at $10 \mathrm{m} / \mathrm{s}$ when it suddenly runs out of gas. a. Can the car make it to the top of the hill by coasting? b. If your answer to part a is yes, what is the car's speed after coasting down the other side?

A $1500 \mathrm{kg}$ car is approaching the hill shown in Figure $\mathrm{P} 10.39$ at $10 \mathrm{m} / \mathrm{s}$ when it suddenly runs out of gas.
a. Can the car make it to the top of the hill by coasting?
b. If your answer to part a is yes, what is the car's speed after coasting down the other side?

Key Concepts

Conservation of Mechanical Energy

This concept refers to the principle that in the absence of non-conservative forces, such as friction, the total mechanical energy of a system remains constant. It underpins problems involving the conversion of energy from one form to another, such as kinetic energy transforming into potential energy or vice versa, and is fundamental in analyzing the motion of objects on inclines or through other energy-changing scenarios.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It increases with height and is central to problems involving objects moving vertically or on slopes, as energy is stored when an object is raised and then converted to kinetic energy as it falls.

Kinetic Energy

Kinetic energy is the energy associated with the motion of an object. It depends on both the mass of the object and the square of its speed. In energy conservation problems, kinetic energy is often compared to potential energy to determine changes in speed or height, especially in systems where energy is exchanged between these two forms.

Transcript

00:01 Hello everyone.

00:02 In this problem, we're first asked to find out if a car that is moving along a straight line with an initial speed of 10 meters per second and has massed 1 ,500 kilograms, can make it to the top of a hill that is located 5 meters above the level at which it's coasting if it runs out of gas.

00:22 So the way to approach this problem is to calculate the final kinetic energy of the car.

00:29 And so we're asked to find what the or what we can find out is what the final velocity of the car is or what the equivalently what the final kinetic energy is.

00:38 So i'll just put this here.

00:39 So this is the equivalent to finding out what the final kinetic energy is.

00:43 So that is what i'm going to do, but you're also able to calculate a final velocity or final speed if that's what you prefer to do.

00:52 So let's see here.

00:54 So we first set up the equation for conservation of energy.

00:57 So we have that the sum of the initial kinetic and potential energies, these two quantities, is equal to the final, the sum of the final kinetic energy and final potential energy, which is the sum of these two quantities.

01:11 And so what we want to find out is if k -e -f, so the final kinetic energy is greater than or equal to zero.

01:18 Because if it is, that means the car is still moving at the top of the hill.

01:23 Okay, so we rearrange for k -e -f.

01:25 We find it is equal to the initial kinetic energy, plus as the initial potential energy minus the final potential energy.

01:32 Okay? and so the initial kinetic energy is just half times mv i squared.

01:38 And the initial potential energy is mg times zero because i have set up the coordinates such that i took the height at which the car was coasting in the beginning to be at the location of zero height and then minus mg h where h is then the height of the hill...

Please give Ace some feedback