Problem A cylindrical culvert is loaded on the bed of a U.S. Forest Service truck (see...

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Problem A cylindrical culvert is loaded on the bed of a U.S. Forest Service truck (see figure below). The truck travels at a constant absolute speed v. The stop is jarred loose when the truck hits a bump in the road. Then, the culvert rolls so that the absolute speed of its center C is ve- Derive a formula for the angular velocity of the culvert in terms of v₁,vc, and (a) r. (b) Derive a formula for the time t at which the culvert is on the verge of rolling off the truck bed, in terms of v, vc, and b. Take t=0 as the instant the culvert begins to roll (see figure). (c) Determine the absolute speed v. of the point P* of the culvert, in terms of v, and vc, at the instant the culvert is on the verge of rolling off the truck. (d) Let v₁ = 12 m/s, vc = 11 m/s, r=450 mm, and b=2 m. Calculate the values of ac, t, and vp Stop- L._. U.S. Forest Service i Problem A cylindrical culvert is loaded on the bed of a U.S. Forest Service truck (see figure below). The truck travels at a constant absolute speed v. The stop is jarred loose when the truck hits a bump in the road. Then, the culvert rolls so that the absolute speed of its center C is ve- Derive a formula for the angular velocity of the culvert in terms of v₁,vc, and (a) r. (b) Derive a formula for the time t at which the culvert is on the verge of rolling off the truck bed, in terms of v, vc, and b. Take t=0 as the instant the culvert begins to roll (see figure). (c) Determine the absolute speed v. of the point P* of the culvert, in terms of v, and vc, at the instant the culvert is on the verge of rolling off the truck. (d) Let v₁ = 12 m/s, vc = 11 m/s, r=450 mm, and b=2 m. Calculate the values of ac, t, and vp Stop- L._. U.S. Forest Service i

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