Explanation:
Given parameters:
Mass of Neil Armstrong = 160kg
Gravitational pull of earth = 10N/kg
Moon's pull = 17% of the earth's pull
Unknown:
Difference between Armstrong's weight on moon and on earth.
Solution:
To find the weight,
Weight = mass x acceleration due to gravity = mg
Moon's gravitational pull = 17% of the earth's pull = 17% x 10 = 1.7N/kg
Weight on moon = 160 x 1.7 = 272N
Weight on earth = 160 x 10 = 1600N
The difference in weight = 1600 - 272 = 1328N
The weight of Armstrong on earth is 1328N more than on the moon.
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b. 460.8 m/s
Explanation:
The relationship between the speed of the wave along the string, the length of the string and the frequency of the note is

where v is the speed of the wave, L is the length of the string and f is the frequency. Re-arranging the equation and substituting the data of the problem (L=0.90 m and f=256 Hz), we can find v:

c. 18,000 m
Explanation:
The relationship between speed of the wave, distance travelled and time taken is

where
v = 6,000 m/s is the speed of the wave
d = ? is the distance travelled
t = 3 s is the time taken
Re-arranging the formula and substituting the numbers into it, we find:

Answer:
the <em>ratio F1/F2 = 1/2</em>
the <em>ratio a1/a2 = 1</em>
Explanation:
The force that both satellites experience is:
F1 = G M_e m1 / r² and
F2 = G M_e m2 / r²
where
- m1 is the mass of satellite 1
- m2 is the mass of satellite 2
- r is the orbital radius
- M_e is the mass of Earth
Therefore,
F1/F2 = [G M_e m1 / r²] / [G M_e m2 / r²]
F1/F2 = [G M_e m1 / r²] × [r² / G M_e m2]
F1/F2 = m1/m2
F1/F2 = 1000/2000
<em>F1/F2 = 1/2</em>
The other force that the two satellites experience is the centripetal force. Therefore,
F1c = m1 v² / r and
F2c = m2 v² / r
where
- m1 is the mass of satellite 1
- m2 is the mass of satellite 2
- v is the orbital velocity
- r is the orbital velocity
Thus,
a1 = v² / r ⇒ v² = r a1 and
a2 = v² / r ⇒ v² = r a2
Therefore,
F1c = m1 a1 r / r = m1 a1
F2c = m2 a2 r / r = m2 a2
In order for the satellites to stay in orbit, the gravitational force must equal the centripetal force. Thus,
F1 = F1c
G M_e m1 / r² = m1 a1
a1 = G M_e / r²
also
a2 = G M_e / r²
Thus,
a1/a2 = [G M_e / r²] / [G M_e / r²]
<em>a1/a2 = 1</em>
Answer:
v_max = (1/6)e^-1 a
Explanation:
You have the following equation for the instantaneous speed of a particle:
(1)
To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:
(2)
where you have use the derivative of a product.
Next, you equal the expression (2) to zero in order to calculate t:
![a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}](https://tex.z-dn.net/?f=a%5B%281%29e%5E%7B-6t%7D-6te%5E%7B-6t%7D%5D%3D0%5C%5C%5C%5C1-6t%3D0%5C%5C%5C%5Ct%3D%5Cfrac%7B1%7D%7B6%7D)
For t = 1/6 you obtain the maximum speed.
Then, you replace that value of t in the expression (1):

hence, the maximum speed is v_max = ((1/6)e^-1)a
Answer:
9 and 3 N
Explanation:
Forces in the same direction sum up to produce the resultant force;
One force subtract the other will give the resultant force when they are in opposite directions;
Lets say one direction is forwards and the opposite backwards;
We have one force, let's say force A, in the forwards direction and another force, force B, acting in the same (forwards) or opposite (backwards) direction;
If B is acting in the same direction, then the resultant force (in this case) will be as follows:
A + B = 12
If B is acting in the opposite direction, then the resultant force will be as follows:
A - B = 6
Summing the two equations will allow us to solve for A:
A + B + (A - B) = 12 + 6
2A = 18
A = 9
Substitute this into either of the above equations and we can solve for B:
(9) - B = 6
B = 9 - 6
B = 3