Two men decide to use their cars to pull a truck stuck in the mud. they attach ropes and one pulls with a force of 615 n at an angle of 31◦with respect to the direction in which the truck is headed, while the other car pulls with a force of 961 n at an angle of 25◦with respect to the same direction. what is the net forward force exerted on the truck in the direction it is headed? answer in units of n.

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)