Answer: d = 4750n/3.1+95n
Explanation:
Using the principle of moment to solve the question.
Sum of clockwise moments = sum of anti clockwise moments
Since there are n identical coins with mass 3.1g placed at point 0cm, 1 coin will have mass of 3.1/n grams
Taking moment about the pivot,
Mass 3.1/n grams will move anti-clockwisely while the mass 95g will move in the clockwise direction.
Since its a meter rule (100cm) the distance from the center mass(95g) to the pivot will be 50-d (check attachment for diagram).
To get 'd'
We have 3.1/n × d = 95 × (50-d)
3.1d/n = 4750-95d
3.1d = 4750n-95dn
3.1d+95dn=4750n
d(3.1+95n) = 4750n
d = 4750n/3.1+95n
We are given a mercury atom in the ground state which absorbs 20 eV of energy. It is then ionized by losing an electron. We need to calculate the kinetic energy that the electron has after ionization.
The initial energy is 20 eV = 20 J/C
The electron charge is = 1.60217662 × 10-19<span> coulombs
To determine the kinetic energy, we can use this equation:
KE = 20 Joules / Coulombs * </span>1.60217662 × 10-19<span> coulombs
KE = 1.25x10^20 Joules
Therefore, the amount of kinetic energy that the electron has after ionization is </span>1.25x10^20 Joules or 1.25x10^17 kJ. <span />
Answer:
The equilibrium temperature is
21.97°c
Explanation:
This problem bothers on the heat capacity of materials
Given data
specific heat capacities
copper is Cc =390 J/kg⋅C∘,
aluminun Ca = 900 J/kg⋅C∘,
water Cw = 4186 J/kg⋅C∘.
Mass of substances
Copper Mc = 235g
Aluminum Ma = 135g
Water Mw = 825g
Temperatures
Copper θc = 255°c
Water and aluminum calorimeter θ1= 16°c
Equilibrium temperature θf =?
Applying the principle of conservation of heat energy, heat loss by copper equal heat gained by aluminum calorimeter and water
McCc(θc-θf) =(MaCa+MwCw)(θf-θ1)
Substituting our data into the expression we have
235*390(255-θf)=
(135*900+825*4186)(θf-16)
91650(255-θf)=(3574950)(θf-16)
23.37*10^6-91650*θf=3.57*10^6θf- +57.2*10^6
Collecting like terms and rearranging
23.37*10^6+57.2*10^6=3.57*10^6θf+91650θf
8.2*10^6=3.66*10^6θf
θf=80.5*10^6/3.6*10^6
θf =21.97°c
Answer:
Since the spring mass system will execute simple harmonic motion the position as a function of time can be written as
'A' is the amplitude = 6 inches (given)
is the natural frequency of the system
At equilibrium we have

Applying values we get

thus natural frequency equals

Thus the equation of motion becomes

At time t=0 since mass is at it's maximum position thus we have

Thus the position of mass at the given times is as follows
1) at

2) at

3) at

4) at

5) at

Answer:
6.32 m/s 18.43° northeast
Explanation:
We express the velocity of hawk as:

We consider positive x towards east and positive y due north. So the magnitude is simply the square root of the square components:
≈
And the angle with respect to the east should be with:
