Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 6.7Ω and 15.9 W, 30.4Ω and 9.12 W, and 16.3Ω and 12.3 W. (a) What is the greatest voltage that the battery can have without one of the resistors burning up? (b) How much power does the battery deliver to the circuit in (a)?


Answer 1


a) greatest voltage = 29.25 V

b) power = 16 W


The total resistance R of the three resistors in series is:

R = (6.7 + 30.4 + 16.3) \Omega = 53.4 \Omega  

a) The greatest current I is the one that will burn the resistor with lower power rating, which is 9.12 W:

P_(max) = I_(max)^2 R = I_(max)^2 30.4\Omega = 9.12W\nI_(max) = 0.54 A

The voltage is:

V_(max)=IR = 0.54*53.4V= 29.25 V

b) When the current is 0.54 A, the power is:

P = RI^2=53.4*0.3 W = 16W

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Sometimes, in an intense battle, gunfire is so intense that bullets from opposite sides collide in midair. Suppose that one (with mass M = 5.12 g moving to the right at a speed V = [08]____________________ m/s directed 21.3° above the horizontal) collides and fuses with another with mass m = 3.05 g moving to the left at a speed v = 282 m/s directed 15.4° above the horizontal. a. What is the magnitude of their common velocity (m/s) immediately after the collision? b. What is the direction of their common velocity immediately after the collision? (Measure this angle in degrees from the horizontal.) c. What fraction of the original kinetic energy was lost in the collision?
The surface tension of a liquid is to be measured using a liquid film suspended on a U-shaped wire frame with an 12-cm-long movable side. If the force needed to move the wire is 0.096 N, determine the surface tension of this liquid in air.
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Nina and Jon are practicing an ice skating routine. Nina is standing still. Jon, who is twice as heavy as Nina, skates toward her, pushing Nina away with force f. Assuming the system is closed, which statement is correct about this system? a. Nina experiences a force equal to f/2. b. Nina experiences a force equal to f^2. c. Nina experiences a force equal to 2f. d. Nina experiences a force equal to f.

The pendulum consists of two slender rods AB and OC which have a mass of 3 kg/m. The thin plate has a mass of 12 kg/m2 . a) Determine the location ӯ of the center of mass G of the pendulum, then calculate the mass moment of inertia of the pendulum about z axis passing through G. b) Calculate the mass moment of inertia about z axis passing the rotation center O.



The answer is below


a) The location ӯ of the center of mass G of the pendulum is given as:

y=(0+(\pi*(0.3\ m) ^2*12kg/m^2*1.8\ m-\pi*(0.1\ m) ^2*12kg/m^2*1.8\ m)+0.75\ m*1.5\ m *3\ kg/m)/((\pi*(0.3\ m) ^2*12kg/m^2-\pi*(0.1\ m) ^2*12kg/m^2)+3\ kg/m^2*0.8\ m+3\ kg/m^2*1.5\ m) \n\ny=0.88\ m

b)  the mass moment of inertia about z axis passing the rotation center O is:

I_G=(1)/(12)*3(0.8)(0.8)^2+ 3(0.8)(0.888)^2-(1)/(2)*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8-\n0.888)^2+(1)/(2)*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8-0.888)^2+(1)/(12)*3(1.5)(1.5)^2+\n3(1.5)(0.888-0.75)^2\n\nI_G=13.4\ kgm^2

c) The mass moment of inertia about z axis passing the rotation center O is:

I_o=(1)/(12)*3(0.8)(0.8)^2+ (1)/(3)* 3(1.5)(1.5)^2+(1)/(2)*(12)(\pi)(0.3)^2(0.3)^2 +(12)(\pi)(0.3)^2(1.8)^2-\n(1)/(2)*(12)(\pi)(0.1)^2(0.1)^2 -(12)(\pi)(0.1)^2(1.8)^2\n\nI_o=13.4\ kgm^2

Final answer:

To solve this problem, calculate the mass of each element of the pendulum, use that information to determine the center of mass, and then apply the parallel axis theorem to calculate the two moments of inertia.


To determine the center of mass and the mass moment of inertia of the pendulum, first we calculate the individual masses of the rods: AB and OC, and the plate. Each rod has a mass of 2 kg (given mass per unit length is 3kg/m and length of each rod is 1 m from the first reference paragraph).

The center of mass ӯ can be determined using the formula for center of mass, averaging distances to each mass element weighted by their individual masses. The mass moment of inertia, also known as the angular mass, for rotation about the z axis through G is determined using the parallel axis theorem, which states that the moment of inertia about an axis parallel to and a distance D away from an axis through the center of mass is the sum of the moment of inertia for rotation about the center of mass and the total mass of the body times D squared.

Finally, the moment of inertia about the z axis passing through the center of rotation O can be calculated again using the parallel axis theorem, with distance d being the distance between points G and O.

Learn more about Mass Moment of Inertia here:


Assume: The bullet penetrates into the block and stops due to its friction with the block.

The compound system of the block plus the

bullet rises to a height of 0.13 m along a

circular arc with a 0.23 m radius.

Assume: The entire track is frictionless.

A bullet with a m1 = 30 g mass is fired

horizontally into a block of wood with m2 =

4.2 kg mass.

The acceleration of gravity is 9.8 m/s2 .

Calculate the total energy of the composite

system at any time after the collision.

Answer in units of J.

Taking the same parameter values as those in

Part 1, determine the initial velocity of the


Answer in units of m/s.


To solve this problem we will start considering the total energy of the system, which is given by gravitational potential energy of the total of the masses. So after the collision the system will have an energy equivalent to,

E_T = (m_1+m_2)gh


m_1= mass of bullet

m_2= Mass of Block of wood

The ascended height is 0.13m, so then we will have to


E_T = (m_1+m_2)gh

E_T = (0.03+4.2)(9.8)(0.13)

E_T = 5.389J

PART B) At the same time the speed can be calculated through the concept provided by the conservation of momentum.

m_1v_1+m_2v_2 = (m_1+m_2)v_f

Since the mass at the end of the impact becomes only one in the system, and the mass of the block has no initial velocity, the equation can be written as

m_1v_1 =(m_1+m_2)v_f

The final velocity can be calculated through the expression of kinetic energy, so

E_T = KE = (1)/(2) (m_1+m_2)v_f^2

v_f = \sqrt{(2E_T)/(m_1+m_2)}

v_f = \sqrt{(2*5.389J)/(0.03+4.2)}

v_f = 1.5962m/s

Using this value at the first equation we have that,

m_1v_1 =  (m_1+m_2)v_f

v_1 =((m_1+m_2)v_f)/(m_1)

v_1 = ((0.03+4.2)(1.5962))/(0.03)

v_1 = 225.06m/s

wo charged spheres are 1.5 m apart and are exerting an electrostatic force (Fo) on each other. If the charge on each sphere decreases by a factor of 9, determine (in terms of Fo) how much electrostatic force each sphere will exert on the other.



F0 / 81


Let the two charges by Q and q which are separated by d.

By use of coulomb's law

F0 = k Q q / d^2      ......(1)

Now the charges are decreased by factor of 9.

Q' = Q / 9

q' = q / 9                 ......(2)

Now the Force is

F' = k Q' q' / d^2

F' = k (Q /9) (q / 9) / d^2

F' = k Q q / 81d^2

F' = F0 / 81      

A electromagnetic wave of light has a wavelength of 500 nm. What is the energy (in Joules) of the photon representing the particle interpretation of this light?



Energy, E=4.002* 10^(-19)\ J


It is given that,

Wavelength of the photon, \lambda=500\ nm=5* 10^(-7)\ m

We need to find the photon representing the particle interpretation of this light. it is given by :


E=(6.67* 10^(-34)* 3* 10^8)/(5* 10^(-7))

E=4.002* 10^(-19)\ J

So, the energy of the photon is 4.002* 10^(-19)\ J. Hence, this is the required solution.

Temperature°F = (9/5 * °C) + 32°
°C = 5/9 * (°F - 32°)
1 pt each. Using the table above as a guide, complete the following conversions. Be sure to show your work to the side:
1. 5 cm = ________ mm
2. 83 cm = ________ m
3. 459 L = _______ ml
4. .378 Kg = ______ g
5. 45°F = ________ °C
6. 80°C = _________ °F


5cm = 50mm
2.83cm = 0.0283m
3.459l = 3459ml
4.378kg = 4378g
5.45f =  - 47.79c
6.80c = 44.24f

A ball is thrown into the air with 100 J of kinetic energy, which is transformed to gravitational potential energy at the top of its trajectory.When it returns to its original level after encountering air resistance, its kinetic energy is __________.

A) more than 100 J.

B) Not enough information given.

C) less than 100 J.

D) 100 J.


To solve this problem we could apply the concepts given by the conservation of Energy.

During the launch given in terms of kinetic energy and reaching the maximum point of the object, the potential energy of the body is conserved. However, part of all this energy is lost due to the work done by the friction force due to friction with the air, therefore

E_T = PE + KE -W_f

The potential and kinetic energy are conserved and are the same PE = KE and this value is equivalent to 100J, therefore

E_T = 100-W_f

The kinetic energy will ultimately be less than 100J, so the correct answer is C.

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