Question

Need help about linear density how is this p(4) in the given pictures below...

Answer 1

please help.

Answer 2

why is it p(4) in the 2nd picture...can someone explain?

Answer 3

The english is not very clear.
when they say
"the linear density... varies directly ... with distance from an external point 2 meters from the end"
they are (trying?) to say
d = k (6-x)

we get 6 from: rod is 4 meters long , so set up the problem so the rod goes from x =0 to x=4. two beyond "the end" puts us at 6.
the "distance from a point on the rod" to the point x=6 is 6-x

Answer 4

they mumble
2 meters from an end, where the density is 5 kg/m

they are saying the density at the x=4 end is 5 kg/m

I would have written it as
"The density at the right-side end is 5 kg/m"

Answer 5

but why is it p(4) in the 2nd picture, how come?

Answer 6

we use that info to find the "constant of variation"
d= k (6-x)
5 = k (6-4)
2.5= k

so the density varies as
d= 2.5 (6-x) from x=0 to x=4

Answer 7

huh? I do not get it why 4 is on the p(4) in the 2nd picture... can you direct to the point...

Answer 8

they are saying rho (which apparently stands for density here) at x=4 is 5
\[ \rho(4) = 5\]

Answer 9

and we know the density at x=4 is 5 because they tell us it is (though the wording is not very clear)

Answer 10

what is that x=4 ? and how come that p(4)=5.

Answer 11

ok ok thanks .

Answer 12

the density is "a function of x"
in other words, you need a "formula" to figure out what the density is at each x location

Based on the problem they decided to put the bar on the x-axis
so its left side is at x=0, and its right side is at x=4 (and the units are meters)

the formula for the density , as a function of x is (after working it out)
\[ \rho(x) = 2.5(6-x) \]

that is typical "math" way to say, some quantity called rho changes with another quantity called x. And we have set up the problem so that x means position along the bar (as long as we keep within the interval x=0 to x=4)

Answer 13

There is a lot that is not stated in this problem, and so a lot of ways to get confused.

Answer 14

but why is p(4) not p(0) is on the 2nd picture...

Answer 15

Maybe if we walk through the question slowly?
"The linear density at any point of a rod 4 m long varies directly as..."

that tells us
1) density will change. Let's call the density rho.
2) "varies directly" means expect an equation rho= k * some variable
where k is the constant of variation
3) the bar is 4 meters long.

At this point I would automatically think: "put the bar on the x-axis"