Question

1. What is the resistance of a toaster that draws a current of 12A when connected to a 120V circuit?
2. What is the speed of an EM wave that has a frequency of 10000 Hz and a wavelength of 0.005m?
3. Two charged pellets, each with a charge of 5C, are located a distance 15m apart. What is the electric force between the two pellets?
4. For problem 26 above, find the work done by gravity if the mass falls a distance 2 meters. If the mass falls for 11 seconds, what is the energy expended by this force?
5. A mass of 5kg is on top of a building of height 10m. Calculate its potential energy.
The mass then falls at a speed of 8 m/s in 4 sec, find its KE and momentum p. What is the Force and impulse the mass transfers to the ground?

Answer 1

1) The resistance can be found according to Ohm's law:

$$R=V/I=120/12=10\space\Omega.$$

2) The speed is

$$v=\lambda\space\nu=0.005\cdot10000=50\text{ m/s}.$$

3) The electric force can be found according to Coulomb's law:

$$F=k\frac{q_1q_2}{r^2}=9\cdot10^9\frac{5\cdot5}{15^2}=1\cdot10^9\text{ N}.$$

4) The work done while the mass was falling from 2 meters:

$$W=mgh=m\cdot9.8\cdot2=19.6m.$$

While the body was falling within 11 s:

$$W=mgh=mg\cdot gt^2/2=m(gt)^2/2=5810m.$$

5) The potential energy is

$$PE=mgh=5\cdot9.8\cdot10=490\text{ J}.$$

The kinetic energy and momentum are:

$$KE=mv^2/2=160\text{ J}.\\ p=mv=40\text{ kg-m/s}.$$

the force and impulse:

$$F=\Delta p/\Delta t=(40-0)/4=10\text{ N}.\\ J=\Delta p=40-0=40\text{ kg-m/s}.$$