A 5.00 kg (m₁) block and a 7.25 kg (m₂) block are hanging on opposite sides of a pulley. Assume that the pulley is frictionless, and the string has negligible mass and cannot be stretched. Using Newton’s second law equation, what will be the equation of the second mass in order to solve for the tension along the string and acceleration of the blocks?
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A 5.00 kg (m₁) block and a 7.25 kg (m₂) block are hanging on opposite sides of a pulley. Assume that the pulley is frictionless, and the string has negligible mass and cannot be stretched. Using Newton’s second law equation, what will be the equation of the second mass in order to solve for the tension along the string and acceleration of the blocks?
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- A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by y = 1/6 sin(8t) + 1/8 cos(8t) where y is the displacement (in feet) from equilibrium of the weight and t is the time (in seconds). (a) Use the identity a sin(Bθ) + b cos(Bθ) = a2 + b2 sin(Bθ + C) where C = arctan(b/a), a > 0, to write the model in the form A) y = (b) Find the amplitude of the oscillations of the weight. (c) Find the frequency of the oscillations of the weightA weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by y as attached where y is the displacement (in feet) from equilibrium of the weight and t is the time (in seconds). (a) Use the identity a sin Bθ + b cos Bθ = √(a2 + b2) sin(Bθ + C) where C = arctan(b/a), a > 0, to write the model in the form y = √(a2 + b2) sin(Bt + C). (b) Find the amplitude of the oscillations of the weight. (c) Find the frequency of the oscillations of the weight.A box with mass M = 13 kg sits on a flat surface and is attached by a massless rope hung over an ideal pulley to another box that is hanging vertically with mass m = 5.0 kg. If the coefficient of kinetic friction between the box and the surface is 0.22, what is the acceleration of the hanging mass?
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