A foolish treasure hunter exploring an ancient tomb climps up a long inclined pa

Question

A foolish treasure hunter exploring an ancient tomb climps up a long inclined passageway only to encounter a gaint spherical boulder (of radius r = 2.0m and mass m = 1.0 * 10^5 kg) that blocks his progress forward. he does his best to dislodge it and, unfortunately for him, succeeds. he runs back down the incline, and the boulder rolls down after him. At the end of the passageway, the boulder is moving along the passageway at v = 30 km/hr.

a) what is the boulder transational kinetic energy?

b) what is the boulder rotational energy?

c) if the passageway is inclined at angle of 30 degrees above the horizontal, how far did the boulder roll along the passageway?

Explanation / Answer

Here ,

speed of boulder , v = 30 km/hr

v = 8.33 m/s

Now,

a)

translational kinetic energy = 0.5 * 1 *10^5 * 8.33^2

the translational kinetic energy is 3.472 *10^6 J

b)

rotational kinetic energy = 0.5Iw^2

rotational kinetic energy = 0.5 * 0.4 * m*r^2 * v^2/r^2

rotational kinetic energy = 0.5 * 0.4 * 1 *10^5 *8.33^2

rotational kinetic energy is 1.388 *10^6 J

c)

Now , for theta = 30 degree

let the distance of d

mg * d *sin(30) = Total kinetic energy

1 *10^5 * 9.8 * d *sin(30) = 1.388 *10^6 + 3.472 *10^6

d = 9.92 m

the distance along the passageway is 9.92 m

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