Two blocks of masses 1 = 700 and 2 = 1100 are connected by a cord of negligible mass and hung over a diskshaped pulley, as shown in the figure. The pulley has a mass of = 1.50 and a radius of = 14 , and rotates about a lightweight axle through its center. The axle itself is hung from the ceiling by two like cords of negligible mass and is held horizontally. The system is released from rest. a) Draw a free-body diagram for each of the blocks and the pulley separately. b) Find the magnitude of the acceleration of the blocks. c) Find the magnitude of the angular acceleration of the pulley. d) Find the magnitude of tensions in the cords, 1, 2, and 3. (See the figure.)
b) 16 cm
Magnification, m = v/u
3 = v/u
⇒ v = 3u
Lens formula : 1/v – 1/u = 1/f
1/3u = 1/u = 1/12
-2/3u = 1/12
⇒ u = -8 cm
V = 3 × (-8) = -24
Distance between object and image = u – v = -8 – (-24) = -8 + 24 = 16 cm
Why are certain things obligations of citizenship instead of responsibilities? atleast 5 sentences please
Please find the answer in the explanation
Responsibilities of citizens are those things citizens are to take care of.
While obligations are those things that are compulsory for the citizens to observe and adhere to.
Why are certain things obligations of citizenship instead of responsibilities?
1.) Because of law and order of the community. It is mandatory for all citizens to obey the law of the land.
2.) Because of the progress and peaceful coexistence of the citizens in the community.
3.) Because of the protection of constitution of the land
4.) To support and defend the constitution
5.) To maintain orderliness and eschew violence.
A research Van de Graaff generator has a 2.00-m diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in MeV when the atom is at the distance found in part b?
a) The potential equation is given by:
k is the electrostatic constant ()
Q is the charge Q = 5mC
r is the radius of the sphere r = 1 m
b) We solve it using the same equation.
Here we need to find r:
c) The relation between difference potential and electrical energy is:
here q is 3e becuase oxygen atom has three missing electrons
I hope it heps you!
Vector A has a magnitude of 6.0 m and points 30° north of east. Vector B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A+ B is given by
The resultant vector is given by .
Let and , both measured in meters. The resultant vector is calculated by sum of components. That is:
The resultant vector is given by .
n Section 12.3 it was mentioned that temperatures are often measured with electrical resistance thermometers made of platinum wire. Suppose that the resistance of a platinum resistance thermometer is 125 Ω when its temperature is 20.0°C. The wire is then immersed in boiling chlorine, and the resistance drops to 99.6 Ω. The temperature coefficient of resistivity of platinum is α = 3.72 × 10−3(C°)−1. What is the temperature of the boiling chlorine?
- 48.55 degree
Resistance increases when temperature increases. This increase is linear and which is defined by the following relation between resistance and temperature
is resistance at temperature t , R₀ is resistance at temperature t₀ , t is rise in temperature and α is temperature coefficient of resistance .
Putting the values we get
125 = 99.6 ( 1 + 3.72x 10⁻³ x t )
t = 68.55
Therefore temperature of boiling chlorine is 20-68.55 = - 48.55 degree celsius .
7) Straws work on the principle of the outside atmospheric pressure pushing the fluid (for example water) up the straw after you have lowered the pressure at the top of the straw (in your mouth). Assuming you could create a perfect vacuum in your mouth, what is the longest vertical straw you could drink water from?
The longest straw will be 10.328 meters long.
The water will rise up to a height pressure due to which will balance the atmospheric pressure.
Pressure due to water column of height 'h'
Equating both the values we get the value of height 'h' as
A large balloon of mass 210 kg is filled with helium gas until its volume is 329 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3. (a) Draw a force diagram for the balloon. (Submit a file with a maximum size of 1 MB.) (b) Calculate the buoyant force acting on the balloon. (Give your answer to at least three significant figures.) 4159 N (c) Find the net force on the balloon. 1524 N Determine whether the balloon will rise or fall after it is released. The balloon will (d) What maximum additional mass can the balloon support in equilibrium? 155 kg (e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)? The balloon and its load will remain stationary. The balloon and its load will accelerate downward. The balloon and its load will accelerate upward. (f) What limits the height to which the balloon can rise?
(a) See figure in attachment (please note that the image should be rotated by 90 degrees clockwise)
There are only two forces acting on the balloon, if we neglect air resistance:
- The weight of the balloon, labelled with W, whose magnitude is
where m is the mass of the balloon+the helium gas inside and g is the acceleration due to gravity, and whose direction is downward
- The Buoyant force, labelled with B, whose magnitude is
where is the air density, V is the volume of the balloon and g the acceleration due to gravity, and where the direction is upward
(b) 4159 N
The buoyant force is given by
where is the air density, V is the volume of the balloon and g the acceleration due to gravity.
In this case we have
is the air density
is the volume of the balloon
g = 9.8 m/s^2 is the acceleration due to gravity
So the buoyant force is
(c) 1524 N
The mass of the helium gas inside the balloon is
where is the helium density; so we the total mass of the balloon+helium gas inside is
So now we can find the weight of the balloon:
And so, the net force on the balloon is
(d) The balloon will rise
Explanation: we said that there are only two forces acting on the balloon: the buoyant force, upward, and the weight, downward. Since the magnitude of the buoyant force is larger than the magnitude of the weigth, this means that the net force on the balloon points upward, so according to Newton's second law, the balloon will have an acceleration pointing upward, so it will rise.
(e) 155 kg
The maximum additional mass that the balloon can support in equilibrium can be found by requiring that the buoyant force is equal to the new weight of the balloon:
where m' is the additional mass. Re-arranging the equation for m', we find
(f) The balloon and its load will accelerate upward.
If the mass of the load is less than the value calculated in the previous part (155 kg), the balloon will accelerate upward, because the buoyant force will still be larger than the weight of the balloon, so the net force will still be pointing upward.
(g) The decrease in air density as the altitude increases
As the balloon rises and goes higher, the density of the air in the atmosphere decreases. As a result, the buoyant force that pushes the balloon upward will decrease, according to the formula
So, at a certain altitude h, the buoyant force will be no longer greater than the weight of the balloon, therefore the net force will become zero and the balloon will no longer rise.
The physics involved in the functioning of helium balloons is based on buoyancy and Archimedes' Principle. The forces at play include the force due to gravity, the buoyant force and the net force, which determines the motion of the balloon. The balloon's height limit is determined by the decrease in air density with altitude.
The several parts of this question are related to the principles of buoyancy and Archimedes' Principle. First, regarding the force diagram for the balloon (part a), it would show two primary forces. The force due to gravity (Fg) acting downwards and the buoyant force (Fb) acting upwards, which is a result of the displacement of air by the balloon. The net force mentioned in part (c) is calculated as the difference between these two forces.
Calculating the buoyant force (part b) involves multiplying the volume of the balloon by the density of the air and the acceleration due to gravity (Fb = V * ρ_air * g). For the net force on the balloon (part c), this is calculated by subtracting the weight of the balloon from the buoyant force (F_net = Fb - Fg). If the net force is positive, the balloon will rise, if it's negative, the balloon will fall, and if it is zero, the balloon will remain stationary.
The maximum additional mass the balloon can support in equilibrium (part d) is calculated using the net force divided by gravity. If the mass of the load is less than this value (part e), the balloon and its load will accelerate upward.
Lastly, the limit to the height to which the balloon can rise (part f) is determined by the decreasing density of the air as the balloon ascends. The buoyant force reduces as the balloon rises because the air density is lower at higher altitudes.