Dynamics of Rigid Bodies (Problem Set)

Assignment ECEA dynamics 1. A rocket is launched vertically at time t=0. The elevation of the rocket is given by y=-0.13ty=−0.13t4+0.13t3+0.12t2 where t is in seconds. Determine the maximum velocity of the rocket and the elevation at which it occurs.

2. A body is released from rest at A and allowed to fall freely. Including the effects of air resistance, the position of the body as a function of the elapsed time is

where vo and to are constants. (a) Derive the expression for the speed v of the body. Use the result to explain why vo is called the terminal velocity (b) Derive the expression of the acceleration a of the body as a function of t and as a function of v.

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3. A bead moves along a straight 60-mm wire that lies along the xaxis. The position of the bead is given by x=2t2−10t mmwhere x is measured from the center of the wire, and t is the time determine(a)the time when the bead leaves the wire; and (b) the distance traveled by the bead from t=0 it leaves the wire.

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4. A particle travels around a circle of radius 4m, changing its speed at a constant rate. At a certain point A, the speed is 3m/s. After traveling another quarter revolution to point B, the speed has increased to 6m/s. Detemine the magnitude of the acceleration of the particle at B.

5. A particle travels along a plane curve from a point A to a point B. The path length between A and B is 2m. The speed of the particle is 4m/s at A and 2m/s at B. The rate of change of the speed is constant. (a) Find the tangential component of the acceleration when the particle is at B (b) If the magnitude of the acceleration at B is 5m/s2, determine the radius of curvature of the path at B.

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6. A particle moves along a plane curve from a point O to a point B. The path length between O and B is 2m. The tangential component of the acceleration is at = 0.04s m/s2, where s is the path coordinate, measured in m from point O. The speed of the particle at O is 2m/s, and the radius of curvature of the path at B is 3m. Determine the magnitude of the acceleration of the particle at B.

7. The coefficient of kinetic friction between the slider and the rod is µ, and the free length of the spring is Lo =b. Derive the expression for the work done by the friction force on the slider as it moves from A to B. Neglect the weight of the slider.

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8. The mans slides the 100-kg crate accross the floor by pulling with a constant force of 200N. If the crate was initially at rest, how far will the crate move before its speed is 1m/s? The coefficient of kinetic friction between the crate and the floor is 0.18.

9. The 1-kg package arrives at A, the top of the inclined roller conveyor, with a speed of 5m/s. After descending the conveyor, the package slides a distance d onthe rough horizontal surface, coming to a stop at B. If the coefficient of kinetic friction between the package and the horiazontal plane is 0.4, determine the distance d.

10.The crossbow is aimed at the sandbag, which is suspended from a cord. At the instant the cord is cut, the crossbow is fired. Show that the bolt will always hit the sandbag, regardless of the initial speed vo of the bolt. (Hint: The velocity of the bolt relative to the sandbag is constant.)

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11.Two cars A and B traveling at constant speeds are in the positions shown at time t =0. Determine (a) the velocity at A relative to B; (b) the position vector of A relative to B as a function of time; and (c) the minimum distance between the cars and the time this occurs.

12.When a stationary car is pointing into the wind, the streaks made by raindrops on the side windows are inclined at θ=15o with the vertical. When the car is driven at 30km/h into the wind, the angle θ increases to 75o. Find the speed of the raindrops

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