The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (a) Com

step 1 Okay, so problem 12 in chapter 13 is a two -part question. Part A is asking us, what is the acce

The mass of Venus is 81.5% that of the earth, and its radius...

Key Concepts

Weight and Gravitational Force

Weight is the force exerted on an object due to gravity and is given by the product of the object's mass and the gravitational acceleration (W = mg). This relationship allows for the comparison of weights on different celestial bodies by taking into account the differences in gravitational acceleration arising from changes in mass and radius.

Newton's Law of Universal Gravitation

Newton's law states that every two masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This principle is fundamental in calculating gravitational acceleration and understanding how mass and radius determine the strength of gravity on the surface of any celestial body.

Gravitational Acceleration

Gravitational acceleration is the acceleration experienced by an object due to the gravitational force exerted by a mass. It is calculated using the formula g = GM/R², where G is the gravitational constant, M is the mass of the body, and R is its radius. This concept explains how variations in a celestial body's mass or radius affect the gravitational pull at its surface.

Transcript

00:01 Okay, so problem 12 in chapter 13 is a two -part question.

00:05 Part a is asking us, what is the acceleration due to gravity on the surface of venus? and we're told two things to help us figure this out.

00:12 We're told that the mass of venus is equal to 81 .5 % of the mass of earth, that the radius of venus is equal to 94 .9 % of the radius of earth.

00:24 So how do we figure out the acceleration due to gravity on different planets? we know that on g or sorry on g on earth it's just equal to g so the acceleration due to gravity on earth well it's just a constant we know what it is um but how do we actually derive this how do we get here so what we do is we take newton second law and we imagine that we have some object in free fall and that it's not experiencing air friction or anything so for an object in free fall with no other forces we're just going to see that the sum of the forces is the force of gravity is equal to mass times acceleration.

01:05 So the next thing we do is we take the universal law of gravitation, which says that the force of gravity between two objects is g times m1 times m2 divided by the radius between those two objects.

01:20 And what we do is we make mass 1, the mass of earth, and we take mass 2 and it's the mass of whatever falling object.

01:29 Object is, or it's the mass of whatever that falling object is.

01:33 I'm just going to leave it as an m, where this is the radius of earth.

01:37 And then what we do is we set this right here equal to that, since the same thing.

01:44 So we're going to get that g, m .e.

01:49 Times m divided by r .e.

01:52 Squared is equal to ma.

01:56 And we can see the mass is cancel.

01:58 So it doesn't actually matter how heavy the falling thing is.

02:01 The acceleration it experiences is constant.

02:06 So here we see this reduces down to gme divided by re squared equals a.

02:16 And this a, well, this is just g or g sub e.

02:22 It's the same thing.

02:24 So in order to find the acceleration due to gravity on venus, so we're going to repeat the same process, but now we're going to have gmv divided by rv squared is equal to, let's see, acceleration due to gravity on venus.

02:48 Okay, so we just take what we have now and we plug in the numbers it gives us...

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