how much work must be done to accelerate an 8.5×10^5 kg train from a) 10m/s to 15m/s b) 15m/s to 20m/s and c) to an Initial stop of 20m/s

Respuesta :

W = ΔE = 1/2 m (v₂ - v₁)²

W work
E kinetic energy
m mass
v₂ final velocity
v₁ initial velocity

Following are the calculation to the given points:

Given:

[tex]a= 8.5 \times 10^5\ kg[/tex]

To find:

points=?

Solution:

Using formula:

[tex]\to W = \Delta E = \frac{1}{2} m (v^2_2 - v^2_1)[/tex]

For point a:

[tex]\to W = \Delta E = \frac{8.5 \times 10^{5}\ kg}{2} (15^2 -10^2)[/tex]

                    [tex]= 4.25 \times 10^{5} \times (225 -100)\\\\= 4.25 \times 10^{5} \times (125)\\\\= 53.125 \times 10^6\ Joules\\\\= 53.125\ MJ\\\\[/tex]

For point b:

[tex]\to W = \Delta E = \frac{8.5 \times 10^{5}\ kg}{2} (20^2 -15^2)[/tex]

                    [tex]= 4.25 \times 10^{5} \times (400 -225)\\\\= 4.25 \times 10^{5} \times (175)\\\\= 74.375 \times 10^6\ Joules\\\\= 74.375\ MJ\\\\[/tex]

For point c:

[tex]\to W = \Delta E = \frac{1}{2} m (v^2_2) - \frac{1}{2} m(v^2_1)[/tex]

[tex]\to W = \Delta E = (\frac{8.5 \times 10^{5}\ kg}{2} (0^2) - \frac{8.5 \times 10^{5}\ kg}{2} (20^2))\\[/tex]

                    [tex]= (4.25 \times 10^{5} \times (0^2) - 4.25 \times 10^{5} \times (400))\\\\= (0) - 4.25 \times 10^{5} \times (400)\\\\= - 1700 \times 10^{5} \\\\= - 170 \times 10^{6} \ Joules \\\\= - 170 \ MJ\\[/tex]

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