The cement bag shown in the figure has a mass of 50 kg and the small pulley has a mass of 2 kg. if the cement bag is pulled upwards with an acceleration of 2 m/s^2, find the force f pulling the rope.

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The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

Madison pushes with a 210-n horizontal force on a 24-kg crate of coffee resting on a warehouse floor. the force of friction on the crate is 74 n. what is the acceleration?