A block m1 of mass 40 kg on a rough horizontal surface is connected to a ball m2 of mass 30 kg by a lightweight cord over a lightweight, frictionless pulley as shown. A force of magnitude 20 N at an angle, 40degrees, with the horizontal is applied to the block as shown, and the block slides to the right. The coefficient of kinetic friction between the block and surface is 0.4. Determine the magnitude of the acceleration of the two objects.

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?