Complete Question
Find the terminal velocity of a spherical bacterium (diameter [tex]2.00 \mu m[/tex] ) falling in water. You will first need to note that the drag force is equal to the weight at terminal velocity. Take the density of the bacterium to be [tex]1.10 *10^{3} \ kg/m^3[/tex]
Answer:
The value is [tex]v_t = 2.38*10^{-6} \ m/s[/tex]
Explanation:
From the question we are told that
The diameter of the spherical bacterium is [tex]d = 2.0\mu m = 2.0 *10^{-6} \ m[/tex]
The density of the bacterium is [tex]\rho =1.10 *10^{3} \ kg/m^3[/tex]
Generally the radius is mathematically represented as
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{2.0 *10^{-6}}{2}[/tex]
=> [tex]r = 1.0*10^{-6}[/tex]
Generally the volume is mathematically represented as
[tex]V = \frac{4}{3} * \pi * r^2[/tex]
=>[tex]V = \frac{4}{3} * 3.142 * (1.0*10^{-6})^3[/tex]
=>[tex]V = 4.189 *10^{-18} \ m^3[/tex]
Generally the mass is mathematically represented as
[tex]m = V * \rho[/tex]
=> [tex]m = 4.189 *10^{-12} * 1.10 *10^{3}[/tex]
=> [tex]m = 4.608 *10^{-15} \ kg[/tex]
Generally the terminal velocity is mathematically represented as
[tex]v_t = \frac{m * g}{ 6\pi * r * \eta}[/tex]
Here [tex]\eta[/tex] is the viscosity of water with value [tex]\eta = 1.005 *10^{-3} \ kg/m\cdot s[/tex]
So
[tex]v_t = \frac{4.608 *10^{-15} * 9.8}{ 6 * 3.142 *1.0*10^{-6} * 1.005 *10^{-3}}[/tex]
=> [tex]v_t = 2.38*10^{-6} \ m/s[/tex]
What best describes a bar magnet
Answer:Bar magnets are permanent magnets as opposed to electromagnets
The spacecraft that have visited the outer planets have all flown close to inner planets (Venus, for example), often more than once, as part of their journeys. What was the primary reason for this?
Answer:
1) The outer planets happened to have been on the far side of the sun, so the shortest route passes the inner planets
Explanation:
All the planets revolve around the sun in a circular orbital. The orbits of Mercury, Venus, Earth, and Mars are tightly held with sun as they are very close to the sun and revolve faster in comparison to outer planet Jupiter, Saturn, Uranus, and Neptune.
Because of the shortest distance between the sun and inner planets, the spacecraft is able to visit the inner planet more than once while outer planets are very far from the sun and revolve around a large orbit, so the spacecraft visited the outer planets less than the inner planet.
Hence, the correct answer is "1".
A solid sphere, with a mass of 3 kg, is rolling across a horizontal floor without slipping. The sphere has 8.4 J of total kinetic energy and has a center of mass velocity of 2 m/s. Calculate the rotational kinetic energy of the solid sphere.
Answer:
2.4 J
Explanation:
The total kinetic energy of the solid sphere = rotational kinetic energy + translational kinetic energy
KE(total) = KE(rot) + KE(trans)
KE(rot) = KE(total) - KE(trans)
Since its total kinetic energy KE' = 8.4 J and its mass, m = 3 kg and the velocity of its center of mass, v = 2m/s, KE(trans) = 1/2mv² = 1/2 × 3 kg × (2 m/s)² = 3 kg × 2 m²/s² = 6 kgm²/s² = 6 J
So, KE(rot) = KE(total) - KE(trans)
Substituting the values of the variables, we have
KE(rot) = 8.4 J - 6 J
KE(rot) = 2.4 J
So, the rotational kinetic energy of the solid sphere is 2.4 J
The rotational kinetic energy of the solid sphere will be "2.4 J".
Kinetic energyAccording to the question,
Total Kinetic energy, KE' = 8.4 J
Mass, m = 3 kg
Center of mass's velocity, v = 2 m/s
Now,
KE(trans) = [tex]\frac{1}{2}[/tex]mv²
By substituting the values,
= [tex]\frac{1}{2}[/tex] × 3 × (2)²
= [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 kgm³/s² or,
= 6 J
We know the relation,
→ KE(rot) = KE(total) - KE(trans)
By putting the values,
= 8.4 - 6
= 2.4 J
Thus the approach above is correct.
Find out more information about kinetic energy here:
https://brainly.com/question/25959744
Starting from rest, a 94-kg firefighter slides down a fire pole. The average frictional force exerted on him by the pole has a magnitude of 750 N, and his speed at the bottom of the pole is 3.1 m/s. How far did he slide down the pole
Given that,
Mass of a firefighter, m = 94 kg
Frictional force, F = 750 N
Speed at the bottom of the pole is 3.1 m/s
It is required to find the distance he slide down the pole.
Using Work-energy theorem,
initial potential energy = final kinetic energy + work done
[tex]mgh=W+\dfrac{1}{2}mv^2[/tex]
[tex]mgh=Fh+\dfrac{1}{2}mv^2[/tex]
Solving for h, such that :
[tex]h(mg-F)=\dfrac{1}{2}mv^2\\\\h=\dfrac{1}{2(mg-F)}mv^2\\\\h=\dfrac{1}{2(94(9.8)-750)}\times 94\times (3.1)^2\\\\h=2.63\ m[/tex]
So, he will slide 2.63 m down the pole.
Find the electric field due to an infinite plane of positive charge with uniform surface charge density
Answer:
Explanation:
The Electric field due to an infinite plane of positive charge with uniform surface charge density can be derived a s follows
let us assume An infinite positively charged sheet and lets take a cylindrical gaussian surface on this surface which is perpendicular to this plane of sheet
we know that positive charge electric field lines will be perpendicular to this sheet surface will be perpendicular to the cylindrical surface
applying gauss law
[tex]Electric field * Area =[/tex] [tex]charge/epsilon\\[/tex]
also sigma=Q/A ⇒ Q=sigma*A
so on one face
E*A=sigma*A/epsilon
also we notice this electric field on one face of the sheet is exactly equal to that on the another face hence electric field will be twice
2E*A=sigma*A/epsilon
final result
[tex]E= sigma/2*epsilon[/tex]
Does heat and temperature depend on the other or are they totally separate ideas? Explain.
Answer:
What heat means in thermodynamics, and how we can calculate heat using the heat ... Scientists define heat as thermal energy transferred between two systems
Explanation:
thermal energy
what is the average speed of a student 100cm/s Bernard 150 cm/s Chloe 50 cm/s Dev 75 cm/s Eduardo 125cm/s
Answer:
100cm/s
Explanation:
Given the speed of the following students;
Bernard 150 cm/s
Chloe 50 cm/s
Dev 75 cm/s
Eduardo 125cm/s
Their average speed of a student will be the mean of their individual speed as shown:
Average speed = 150+50+75+125/4
Average speed = 400/4
Average speed = 100
Hence the average speed of a student is 100cm/s
what is it? and explain pls
The velocity at which an object is sent moving and the mass of the object both play a hand in the level of kinetic energy that object produces. Mass and kinetic energy have a positive relationship, which means that as mass increases, kinetic energy increases, if all other factors are held constant.
A 11.8-kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of 10.4 m/s, determine the following. (a) the translational kinetic energy of its center of gravity J (b) the rotational kinetic energy about its center of gravity J (c) its total kinetic energy J
Answer:
1. 638.144j
2. 319.072 j
3. 957.216 j
Explanation:
M = 11.8 kg cylinder
V = speed of center of gravity = 10.4m/s
A.
Translational kinetic energy
= 1/2mv²
1/2x 11.8kg x 10.4²
= 11.8x108.16/2
= 1276.288/2
= 638.144 J
This is the translational energy
B.
Rotational energy
1/2Iw²
I = mv²/2
w = v/r
When we substitute
1/2[mv²/2][v/r]²
= 1/4mv²
= 1/4 x 11.8 x 10.4²
= 1276.288/4
= 319.072
This is the rotational energy
C
Total kinetic energy.
We add the values of A and B above to get this.
638.144 J + 319.072 J
= 957.216J
the weight of a box having a mass of 100kg is blank N.
Answer:
What is the answer we are supposed to be finding?
Explanation: Your answer is 980.7 if you are converting kilograms to Newtons