Some more practice with tensor products. îfa8b is the tensor product of an observable a = at acting in hilbert space and bb acting hilbert space and (2) is any real-valued function, then f(a3 b) is an observable acting on ж. зно. true or false? f(a b) explicit counter-example. f(a) f(b). if true, demonstrate that it is true. if false, provide an explicit counter example.

Under the action of a constant force an object accelerates at 7.8 m/s2. what will the acceleration be if (a) the force is halved? (b) the object's mass is halved? (c) the force and the object's mass are both halved? (d) the force is halved and the object's mass is doubled?

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?

Aball of mass 0.3kg is released from rest at a height of 8m.how fast is it going when it hits the ground? accleration due to gravity is g=9.8m/s