Answer:
Wn = 9.14 x 10¹⁷ N
Explanation:
First we need to find our mass. For this purpose we use the following formula:
W = mg
m = W/g
where,
W = Weight = 675 N
g = Acceleration due to gravity on Surface of Earth = 9.8 m/s²
m = Mass = ?
Therefore,
m = (675 N)/(9.8 m/s²)
m = 68.88 kg
Now, we need to find the value of acceleration due to gravity on the surface of Neutron Star. For this purpose we use the following formula:
gn = (G)(Mn)/(Rn)²
where,
gn = acceleration due to gravity on surface of neutron star = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
Mn = Mass of Neutron Star = Mass of Sun = 1.99 x 10³⁰ kg
Rn = Radius of neutron Star = 20 km/2 = 10 km = 10000 m
Therefore,
gn = (6.67 x 10⁻¹¹ N.m²/kg²)(1.99 x 10³⁰ kg)/(10000)
gn = 13.27 x 10¹⁵ m/s²
Now, my weight on neutron star will be:
Wn = m(gn)
Wn = (68.88)(13.27 x 10¹⁵ m/s²)
<u>Wn = 9.14 x 10¹⁷ N</u>
Answer:
R = 715.4 N
L = 166.6 N
Explanation:
ASSUME the painter is standing right of center
Let L be the left rope tension
Let R be the right rope tension
Sum moments about the left end to zero. Assume CCW moment is positive
R[5] - 20(9.8)[5/2] - 70(9.8)[5/2 + 2] = 0
R = 715.4 N
Sum moments about the right end to zero
20(9.8)[5/2] + 70(9.8)[5/2 - 2] - L[5] = 0
L = 166.6 N
We can verify by summing vertical forces
116.6 + 715.4 - (70 + 20)(9.8) ?=? 0
0 = 0 checks
If the assumption about which side of center the paint stood is incorrect, the only difference would be the values of L and R would be swapped.
Answer:
F = 614913.88 N
Explanation:
We are given;
Mass of pile driver; m = 1800 kg
Height of fall of pole driver; h = 4.6 m
Depth driven into beam; d = 13.6 cm = 0.136 m
Now, from energy equations and applying to this question, we can write that;
Workdone = Change in potential energy
Formula for workdone is; W = F × d
While the average potential energy here is; W = mg(h + d)
Thus;
Fd = mg(h + d)
Where F is the average force exerted by the beam on the pile driver while in bringing it to rest.
Making F the subject, we have;
F = mg(h + d)/d
F = 1800 × 9.81 × (4.6 + 0.136)/0.136
F = 614913.88 N
Remember that sound intensity decreases in inverse proportion to the distance squared. So, to solve this we are going to use the inverse square formula:
![\frac{I_{2} }{I_{1}}= (\frac{d{2} }{d_{1}})^2](https://tex.z-dn.net/?f=%20%5Cfrac%7BI_%7B2%7D%20%7D%7BI_%7B1%7D%7D%3D%20%28%5Cfrac%7Bd%7B2%7D%20%7D%7Bd_%7B1%7D%7D%29%5E2%20%20)
where
![I_{2}](https://tex.z-dn.net/?f=I_%7B2%7D)
is the intensity at distance 2
![I_{1}](https://tex.z-dn.net/?f=I_%7B1%7D)
is the intensity at distance 1
![d_{2}](https://tex.z-dn.net/?f=d_%7B2%7D)
is distance 2
![d_{1}](https://tex.z-dn.net/?f=d_%7B1%7D)
is distance 1
We can infer for our problem that
![I_{1}=270](https://tex.z-dn.net/?f=I_%7B1%7D%3D270)
,
![d_{1}=1](https://tex.z-dn.net/?f=d_%7B1%7D%3D1)
, and
![d_{2}=3](https://tex.z-dn.net/?f=d_%7B2%7D%3D3)
. Lets replace those values in our formula to find
![I_{2}](https://tex.z-dn.net/?f=I_%7B2%7D)
:
![\frac{I_{2} }{I_{1}}= (\frac{d{2} }{d_{1}})^2](https://tex.z-dn.net/?f=%20%5Cfrac%7BI_%7B2%7D%20%7D%7BI_%7B1%7D%7D%3D%20%28%5Cfrac%7Bd%7B2%7D%20%7D%7Bd_%7B1%7D%7D%29%5E2%20)
![\frac{I_{2} }{270} =( \frac{1}{3} )^2](https://tex.z-dn.net/?f=%20%5Cfrac%7BI_%7B2%7D%20%7D%7B270%7D%20%3D%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%5E2)
![\frac{I_{2} }{270} = \frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7BI_%7B2%7D%20%7D%7B270%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D%20)
![I_{2}= \frac{270}{9}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%20%5Cfrac%7B270%7D%7B9%7D%20)
![I_{2}=30](https://tex.z-dn.net/?f=I_%7B2%7D%3D30)
dB
We can conclude that the intensity of the sound when is <span>3 m from the source is
30 dB.</span>