IB Physics Final Review 3/4

A battery of emf 16.7 V and internal resistance 2.8 ohms is connected to a load resistor of resistance 7.6 ohms. Calculate the power delivered to the external load.

a. ((16.7/10.4))^2*7.6

An electric motor that is connected to a 13.4 V supply is able to raise a 0.46 kg load through a distance of 2.6 m in 7.3 seconds. The motor is 40 percent efficient. Calculate the average current in the motor while the load is being raised.

a. (0.46*9.8*2.6/7.3/13.4/0.4)*1000= 299.550194234308

Find R_{AB} in the circuit shown given that R_1 = 8 k\Omega, R_2 = 8 k\Omega, R_3 = 2 k\Omega, R_4 = 8 k\Omega and R_5 = 1 k\Omega

a. (1/((1/(1/((1/8)+(1/1))+8))+2))+8

Two point charges of magnitude +6.8 u C and +1.3 u C are 2.4 m apart in a liquid that has a permittivity \varepsilon = 2.2 x 10^{-11}{C^2}/{N * m^2}

a. (1/(4*pi*2.2E-11))*(6.8E-6)*(1.3E-6)/2.4^2*1000= 5.55133245317375

A potential divider consists of two resistors in series with a battery of V_{source} = 10 V. The resistors have resistance R_1 = 11 \Omega and R_2 = 17 \Omega. Calculate the potential difference across each resistor as well as the current flowing through them Vr1 Vr2 I

a. (10/28)*11 b. (10/28)*17 c. 10/28

Calculate the orbital period of Jupiter about the Sun if the mass of the Sun is 2 \times 10^{30} kg and the radius of Jupiter's orbit is 7.8 \times 10^{11} m

a. (2*pi*7.8E11)/(sqrt(6.7E-11*2E30/7.8E11))

Calculate the Gravitational Force of attraction between a proton of mass 1.67 \times 10^{-27} kg and an electron of mass 9.11 \times 10^{-31} kg when they are 3.3 \times 10^{-10} m apart (the distance 1 \times 10^{-10} m is so common as to have its own name - the Angstrom \AA). Calculate the magnitude of the Electric Force of attraction between the proton and electron. Next, take the ratio of the Electric Force to the Gravitational Force. This should give a clear indication as to why the Gravitational Force is termed a weak force while the nuclear force is deemed a strong force

a. (6.67E-11*1.67E-27*9.11E-31)/(3.3E-10)^2 b. (9E9*(1.6E-19)^2)/(3.3E-10)^2/(6.7E-11)*0*0/(3.3E-10)^2

A uniform wire has a radius of 0.22 mm and a length of 2.1 m. Calculate the resistance of the wire if its resistivity is 7.8 \times 10^{-7} \Omega \cdot m. Always assume a cylindrical wire with a circular cross-section unless otherwise specified. Calculate the resistance of a block of copper that has a length of 12.1 mm with a width of 0.15 mm and a thickness of 10.1 mm. The resistivity of copper is 1.7 \times 10^{-8} \Omega \cdot m

a. (7.8E-7*2.1)/(0.22E-3^2*pi)

Two point charges, a +45 nC charge X and a +28 nC charge Y are separated by a distance of 0.5 m. (a) Calculate the resultant electric field strength at the midpoint between the charges. (b) Calculate the distance from X at which the electric field strength is zero. (c) Calculate the magnitude of the electric field strength at the point P on the diagram below.

a. (9E9(45E-9)/0.25^2)-(9E9(28E-9)/.25^2)= 2448 b. (0.5)*sqrt(45/28)/(1+sqrt(45/28))*1000= 279.515332394185 c. sqrt(((9E9*45E-9)/0.4^2)^2+((9E9*28E-9)/0.3^2)^2)= 3774.54984898862

A straight wire lies in a uniform magnetic field as shown in the image above. The current in the wire is 4 amperes and the wire is at an angle of 25.2 degrees to the magnetic field. The force per unit length on the conductor is 0.68 N/m. Determine the magnetic field strength.

a. 0.68/4/sin(25.2*pi/180)*1000

To calculate the magnitude of the magnetic field strength in a current carrying wire, we may also use the equation in the image above. The value "mu-naught" or \mu_0 is called the permeability of free space. It is reasonable to see that the further we are away from the wire, the lower the magnitude (or strength or intensity) of the field. If the wire conducts in a vacuum (the value in air is very close to the vacuum value), the permeability of free space is \mu_0 = 1.2566370614... \times 10^{-6} \frac{N}{A^2}. How strong is the magnetic field if you are standing 1.14 m away from an un-shielded wire carrying 37.6 A

a. 1.2566370614E-6*37.6/(2*pi*1.14)*10^6 b. 1/sqrt(8.85E-12*(4pi*10^-7))

An organ pipe is open only at one end. If in the first harmonic, the length of the pipe is 1.37 m, and the speed is 1.35 km/s, what is the frequency? A different organ pipe, also only open at one end, is vibrating at the 3rd harmonic with a frequency of 3.18 Hz and the length of the pipe is 4.42 m, what is the speed of the sound wave?

a. 1350/(1.37*4)= 246.350364963504 b. (3.18)*(2/3*2*4.42)= 18.7408

Four resistors of resistance, R_1 = 13 \Omega, R_2 = 13 \Omega, R_3 = 29 \Omega, and R_4 = 12 \Omega are connected as shown in the image. Calculate the equivalent resistance across nodes A and B.

a. 144/26+(29*12)/(29+12)

Three resistors of resistance, 2 \Omega, 12 \Omega, and 28 \Omega are connected. Calculate the total resistance of the three resistors when they are connected (a) in series. (b) in parallel.

a. 2+12+28 b. 1/(1/2+1/12+1/28)

A cell has a capacity of 2400 mA h. Calculate the number of hours for which it can supply a current of 3.1 mA

a. 2400/3.1

A lightning bolt carrying 15000 A lasts for 50 \mu s. If the lightning strikes a tractor and the tires are assumed to be perfect insulators, the charge deposited on the tractor is 0.75 C. If the a lightning bolt carrying 25000 A lasts for 60 \mu s, determine the charge deposited on the tractor if the tires are assumed to be perfect insulators.

a. 25000*60E-6= 1.5

A cell has a capacity of 2600 mA h with 6.4 V across its terminals. There are 8 smaller batteries that comprise the cell. Calculate the number of hours it will take to discharge if a high-power load resistor of 10 \Omega is connected to the battery.

a. 2600/(6.4/10*1000) b. 4.0625*7/8

A cell of emf 7 V and internal resistance 2.6 \Omega is connected to a 7.4 \Omega resistor. Calculate: (a) the current in the cell (b) the terminal pd across the cell (c) the energy lost in the cell when charge flows for 11 s

a. 7/(7.4+2.6) b. 0.7*7.4 c. 0.7*2.6*0.7*11

A model for a standard two D-cell flashlight is shown below. Find the power dissipated, P, in the lamp given the resistance of lamp is 4 \Omega

a. 9/4

An oxygen nucleus has a charge of +8e (or 8 times the charge of one proton). Calculate the magnitude of the electric field strength at a distance of 0.63 nm from the nucleus

a. 9E9(1.6E-19*8)/(0.63E-9)^2= 29024943310.6576

Calculate the currents in the attached circuit if the source voltage is 20 V, R_1 is 200 \Omega, R_2 is 400 \Omega, and R_3 is 630 \Omega, and R_4 is 930 \Omega. I1 I2 I3 I4

a. I1= 20/(200+1/(1/400+1/630+1/930)) I2= (20-(0.0507998488474619*200))/400 I3= (20-(0.0507998488474619*200))/630 I4= (20-(0.0507998488474619*200))/930

Using the passive sign convention, determine the missing quantity in the following circuits. a. P=65W and V=22V b. V=7.5V and I=6A

a. I=65/22 b. 7.5*-6

A large clock on a building has a minute hand that is 4.6 m long. Calculate (a) the angular speed of the minute and second hands. (b) the angular displacement, in radians, in the time periods from 12 noon to 12:38 PM and 12 noon to 2:23 PM. (c) the linear speed of the tip of the minute hand.

ai. 2*pi/3600 ii. 2*pi/60 bi. 38/60*2pi ii. 143/60*2pi c. 4.6*2pi/3600