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Dynamics

PROBLEM 1. When a car accelerates, the normal force at the tire/ground interface changes, increasing at the rear tires and decreasing at the front. Does the same occur for the Batmobile? The Batmobile is shown, along with its jet-engine propulsion system (please see the attachment). Assume an acceleration of 0.9g. Neglect ground/tire forces in the i direction. L1 = 1m, L2 = 1.8m, and h = 0.65m.

How do the normal forces change from their static values?

PROBLEM 2. A gymnast competing at the Olympics is performing a routine on the uneven bars. After completing a flip, she approaches the higher of the two bars with a speed v0 at an angle beta; with respect to the ground. Assume that her body is aligned with the horizontal at approach. The gymnast has a mass m, and her body has a length of L with her hands and legs stretched out. Find the gymnast's angular speed just after grabbing on to the bar?

PROBLEM 3. A hoop with mass m = 10kg and radius r = 0.4m is rolled down a rough surface toward a spring of stiffness k = 1500N/m. The surface is angled at 45 degree with respect to the horizontal, and the hoop's mass center G is initially d = 4m from the spring. The hoop rolls without slip down the incline, and its moment of inertia about G is IG = mr^2. Find the initial speed v0 of the hoop's mass center if the maximum compression of the spring is 0.7m?

(Please see the attachment for figs.)

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