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4 0

3 years ago

A train locomotive is pulling two cars of the same mass behind it. Determine the ratio of the tension in the coupling (think of

Anna007 [38]

Answer:

The ratio is $\frac{F_{T1}}{F_{T2}} = 2$

Explanation:

The diagram for this question is shown on the first uploaded image

Here we are assume the acceleration of the train is a

which makes the acceleration of each car a

From the question we are told that

Considering the second car

The force causing it s movement is mathematically represented as

$F_{T2} = ma$

Considering the first car

The force causing it s movement is mathematically represented as

$F = F_{T1} -F_{T2} = ma$

=> $F_{T1} -ma = ma$

=> $F_{T1} = 2 ma$

=> $\frac{F_{T1}}{ma} = 2$

=> $\frac{F_{T1}}{F_{T2}} = 2$

7 0

2 years ago

If rho(x,y) is the density of a wire (mass per unit length), then

lidiya [134]

Answer:

See description

Explanation:

With the given information we have:

$x(t) = 1 + cos(t)\\ y(t)=sin(t)\\ \rho(x,y) = 3x$

the interval is $[0,\pi ]$

now the mass $m$ has the given expression:

$m = \int \rho(x,y) dS$

we will use the formula for a line integral and let:

$dS=\sqrt{x'(t)^2 + y'(t)^2}=\sqrt{cos(t)^2 + sin(t)^2}dt=dt$

therefore we have:

$m=\int \rho(x,y)dS=\int\limits^\pi_0 {3*x}dS=\int\limits^\pi _0{3*(1+cos(t))dS\\=\int\limits^\pi _0{3*(1+cos(t))dt$

we solve the integral:

$m=3*\int\limits^\pi _0{(1+cos(t))dt= 3*(t+sin(t))\limits^\pi _0=3*\pi=9.42$

7 0

2 years ago