The mass of a car is 1500 kg. The shape of the body is such...

Key Concepts

Power Calculation

Power in the context of mechanics is defined as the rate at which work is done, which can be calculated as the product of force and velocity. In scenarios where multiple forces such as drag and gravitational components act against the motion, the total power requirement is determined by the sum of the individual forces multiplied by the velocity of the object.

Unit Conversion

Accurate unit conversion is critical in physics and engineering problems to ensure all quantities are expressed in consistent units before performing calculations. Converting speeds, masses, and angles into their respective SI units is essential for correctly applying formulas and obtaining valid results.

Aerodynamic Drag

Aerodynamic drag is the resistive force that a moving object experiences due to air resistance. It is typically modeled as being proportional to the square of the velocity of the object and depends on factors such as air density, the drag coefficient, and the frontal area. This concept is essential in dynamics and fluid mechanics when evaluating the forces that oppose motion in fluids.

Gravitational Force on an Incline

When an object moves on an inclined surface, the gravitational force can be resolved into two components: one perpendicular to the surface and one parallel to it. The component parallel to the incline, given by mg sin?, is responsible for either aiding or opposing the motion of the object and must be overcome by applied forces, especially in uphill motion.

Transcript

00:01 Okay, so definitely the best thing to do here is to start with a force diagram and to kind of picture what's happening here.

00:06 So if i have this little hill, it's actually a pretty gentle slope.

00:14 Okay, so this is 3 .2 degrees.

00:19 Okay, and i'm going to imagine a little truck on it or car or whatever vehicle they say that it is.

00:30 So what we're thinking is what are the forces on it, right? so first i have the force of its weight.

00:39 Well, actually, let me back up.

00:41 I have, yes, i have the force of its weight towards the center of the earth.

00:46 I also have the force, but basically the component of that weight that's actually going to want to move us down the hill, make it roll down the hill, which is m .g.

00:57 Sign of 3 .2.

01:00 I also have the force of dragon.

01:05 Force of drag.

01:08 Pushing us forward, i have the force from the actual motor itself.

01:15 So i also want it to move at a constant velocity, which, if you recall, means that there's zero net force.

01:22 So that means that for my equations, i want net force equals zero, which will also equal the force of the motor.

01:31 Assuming, by the way, assuming we consider up the slope positive direction, down the slope negative direction.

01:38 That's kind of help right here.

01:39 So it's a positive force going up the slope due to the motor.

01:42 A negative force of drag pulling us back, or rather pushing us back, and a negative force of gravity pulling us down the hill, which stated is 3 .2.

02:00 Okay, so i also want to know, i'm going to mention it now, that power equals work over time, okay, which remember that work is change in energy, but assuming we're starting from rest, that's basically just energy, right? another way we can think of this is force times distance.

02:26 Do not confuse this with this, right? this is force subdistance.

02:30 F subd, meaning the force to the direct, but this is force times the actual distance i've traveled over time.

02:38 And i'm also going to go a little bit further.

02:40 We know that because we're moving at a constant velocity, the distance is just velocity times time.

02:47 So really, this is just velocity times time over time.

02:52 So in this particular situation, because velocity is constant, power is just force times velocity, which makes things way easier.

03:01 So, okay, let's see here.

03:04 What are we going to do? so i have this equation right here.

03:08 I'm going to solve for the force of the motor.

03:11 The force of the motor is the force to drag plus m .g sine of 3 .2.

03:27 So this is my force, right? so i know if i just multiply by my velocity, i'm going to have power, right? so i can say force times velocity equals power, right, which is equal to this whole thing times velocity.

03:43 So i'm going to have force 2 to drag plus mg sign of 3 .2 times the velocity.

03:55 Okay...

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