L2IC2.2-truck-revised

L2IC2.2-truck-revised - The 20 Mg truck starts from rest...

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The 20 Mg truck starts from rest and pulls the 2000 kg crate as shown in the figure. The 20 o angle between the rope and the ground is constant, and the tension in the rope is measured using an S-type force transducer. This force was found to follow the equation F = 90 t 2 (where t is time in seconds). The coefficient of static friction is μ s = 0.4 and the coefficient of kinetic friction is μ k = 0.3. What is the acceleration of the crate as a function of time? 20 o F f N W ma x 20 o Problem Type: Find: Given: m, F(t), μ s , μ k a(t) Asks for the relationship between force and acceleration, so Newton’s second law problem First step? FBD and MAD – do it x y Equations of motion 0 x y Does the box move right away? No, the towing force must be large enough to overcome the static friction. Impending motion means the friction force is at a max ( μ s N) and acceleration is zero. How do I express this mathematically? (1) Until motion occurs, friction exactly counteracts the Fx force Means impending motion.
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