A 25-m-long train rides in a slightly sloped track as shown in Figure 3. Assume

Question

A 25-m-long train rides in a slightly sloped track as shown in Figure 3. Assume that: (i) the train mass is 850 kg/,; (ii) the t rain speeds at A and B are 65 and 58 km/h, respectively. Determine the constant friction force per unit length exerted by the tracks on the train. A delivery worker weighing 75 kg (package included) jumps from his truck onto the ground with a velocity vector v as shown in Figure 4. Determine the impulse exerted by the ground onto the worker so that the final velocity vector is v'

Explanation / Answer

3. initial speed, u = 65 km/h = 65 x1000m / 3600s = 18.06 m/s

final speed, v = 58 km/h = 16.11 m/s

distance,d = h/sin@ = 12 / sin3 = 229.3 m

using v^2 - u^2 = 2ad

16.11^2 - 18.06^2 = 2(a)(229.3)

a = - 0.145 m/s^2

along the incline,
Fnet = ma

- f - mgsin3 = ma

- f - (850 x 9.8 x sin3) = 850 x (-0.145)

f = - 312.71 N

friction force per unit length = 312.71 / 25 = 12.51 N ....upward

4.
Impulse = change in momentum

     = m (v' - v)

    = 75 [ (0.01j + 0k ) - (-0.02j + 0.02k)]

      = 2.25j - 1.5k   kg m /s

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