Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of ion source, hydrogen atoms (i. e., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. Electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionize it. One such source uses a magnetic field of 90 mTmT, and the electrons' kinetic energy is 1.4 eV. Required:
If the electrons travel in a plane perpendicular to the field, what is the radius of their orbits?

A2.50 × 105 w motor is used for 26.4 s to pull a boat straight toward shore. how far does the boat move toward shore if a force of 4.20 × 104 n is applied by the motor?

Learning goal: to understand newton's 1st law. newton's principia states this first law of motion: an object subject to no net force maintains its state of motion, either at rest or at constant speed in a right line. this law may be restated as follows: if the sum of all forces acting on an object is zero, then the acceleration of that object is zero. mathematically this is just a special case of the 2nd law of motion, f⃗ =ma⃗ , when f⃗ =0. when studying newtonian mechanics, it is best to remember the 1st law in two ways: if the net force (i.e., sum of all forces) acting on an object is zero, the object will keep moving with constant velocity (which may be zero). if an object is moving with constant velocity, that is, with zero acceleration, then the net force acting on that object must be zero. complete the following sentences to see if you can apply these ideas. part a if a car is moving to the left with constant velocity, one can conclude that

How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57×10−21 newtons?