EGBE261: Biomechanics 2 Homework from Chapter 2: Motion of a Point

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1 EGBE261: Biomechanics 2 Homework from Chapter 2: Motion of a Point Use Straight-Line motion equations for the following problems: 2.8. The mechanism causes the displacement of point P to be s = 0.2 sin (πt) m, where t is in seconds and the argument πt is in radians. Determine the velocity and acceleration of P at t = 3.8 s At t = 0, a motorist traveling at 100 km/hr sees a deer standing in the road 100 m ahead. After a reaction time of 0.3 s, he applies the brakes and decelerates at a constant rate of 4 m/s 2. If the deer takes 5 s from t = 0 to react and leave the road, does the motorist miss him? Zoologists studying the ecology of the Serengeti Plain estimate that the average adult cheetah can run 100 km/hr and the average springbuck can run 65 km/hr. If the animals run along the same straight line, start at the same time, and are each assumed to have constant acceleration and reach top speed in 4 s, how close must a cheetah be when the chase begins to catch a springbuck in 15 s? 2.38: θ = 1 rad, dθ/dt = -2 rad/s, and d 2 θ/dt 2 = 0. What are the velocity and acceleration of P relative to O?

2 2.50. A rocket sled starts from rest and accelerates at a = 3t 2 m/s 2 until its velocity is 1 km/s. It then hits a water brake, and its acceleration is a = v2 m/s until its velocity decreases to 500 m/s. What total distance does the sled travel? A spring-mass oscillator consists of a mass and a spring. The coordinate s measures the displacement of the mass relative to its position when the spring is unstretched. If the spring is linear, the mass is subjected to a deceleration proportional to s. Suppose that acceleration a = -4sm/s 2 and that you give the mass a velocity v=1 m/s in the position s = 0. a) How far will the mass move to the right before the spring brings it to a stop? B) What will be the velocity of the mass when it has returned to the position s = 0? If the pitching wedge the golfer is using gives the ball an initial angle of θ 0 =50, what range of velocities v 0 will cause the ball to land within 3 ft of the hole?

3 2.78. A baseball pitcher releases a fastball with an initial velocity of 90 mi/hr. Let θ be the initial angle of the ball s velocity vector above the horizontal. When it is released, the ball is 6 ft above the ground and 58 ft from the batter s plate. The batter s strike zone extends from 1 ft 10 in above the ground to 4 ft 6 in above the ground. Determine whether the ball will hit the strike zone a) if θ = 1, and b) if θ = 2. Use curvilinear strategies to answer the following problems Point P moves upward in the slot with velocity v = 300 e t (mm/s). When y = 150 mm, what are dy/dt and d 2 y/dt 2?

4 A boy rides a skateboard on the concrete surface of an empty drainage canal described by the equation shown. He starts at y = 20 ft, and the magnitude of his velocity is approximated by v 2( 32.2)( 20 y) = ft/sec. What is the instantaneous radius of curvature of his path when he reaches the bottom? What is the normal component of his acceleration when he reaches the bottom? The slotted bar rotates with constant angular velocity ω = 10 rad/s and the radial position of the follower A is determined by the profile of the stationary cam. The path of the follower is described by the polar equation r = cos 2θ ft. Determine the acceleration of the cam follower when θ=30, in terms of polar coordinates and in terms of Cartesian coordinates.

5 The bars OA and AB are each 400 mm long and rotate in the x-y plane. OA has a counterclockwise angular velocity of 10 rad/s and a counterclockwise angular acceleration of 2 rad/s2. AB has a constant counterclockwise angular velocity of 5 rad/s relative to the nonrotating coordinate system. What is the acceleration of B relative to A? In the above problem, what is the acceleration of B relative to the fixed point O? To be solved using Matlab: In an industrial process, the sprayer projects a stream of liquid onto the horizontal surface. An engineer wants to place the sprayer at a horizontal position xe that maximizes its coverage of the horizontal surface. That is, he wants to maximize the distance xs xe reached by the spray. The angle θ 0 can be varied, but the spray velocity v 0 =3 m/s is fixed. The dimensions H = 0.2 m, L = 9.12 m, and h = 0.06 m. If the droplets of the spray are treated as projectiles, what is the desired position x e? Please submit a printout of your matlab code to receive class participation credit next week. Be sure to include your name, Engineering number, and Biomechanics 2 number in the top of the code.