Answer:
m≈501.57 g
Explanation:
The density formula is:
d=m/v
Let’s rearrange the formula for m. m is being divided by v. The inverse of division is multiplication, so multiply both aides by v.
d*v= m/v*v
d*v=m
The mass can be found by multiply the density and the volume.
m=d*v
The density is 1.06 grams per milliliter and the volume is 473.176 milliliters.
d= 1.06 g/mL
v= 473.176 mL
Substitute the values into the formula.
m= 1.06 g/mL * 473.176 mL
Multiply. When multiplying, the mL will cancel out.
m= 501.56656 g
Let’s round to the nearest hundredth. The 6 in the thousandth place tells us to round the 6 to a 7 in the hundredth place.
m ≈501.57 g
The mass is about 501.57 grams.
Answer:
a)-1.014x
J
b)3.296 x
J
Explanation:
For Sphere A:
mass 'Ma'= 47kg
xa= 0
For sphere B:
mass 'Mb'= 110kg
xb=3.4m
a)the gravitational potential energy is given by
= -GMaMb/ d
= - 6.67 x
x 47 x 110/ 3.4 => -1.014x
J
b) at d= 0.8m (3.4-2.6) and
=-1.014x
J
The sum of potential and kinetic energies must be conserved as the energy is conserved.
+
=
+ 
As sphere starts from rest and sphere A is fixed at its place, therefore
is zero
=
+ 
The final potential energy is
= - GMaMb/d
Solving for '
'
=
+ GMaMb/d => -1.014x
+ 6.67 x
x 47 x 110/ 0.8
= 3.296 x
J
1) 29.4 N
The force of gravity between two objects is given by:

where
G is the gravitational constant
M and m are the masses of the two objects
r is the separation between the centres of mass of the two objects
In this problem, we have
(mass of the Earth)
(mass of the box)
(Earth's radius, which is also the distance between the centres of mass of the two objects, since the box is located at Earth's surface)
Substituting into the equation, we find F:

2) 
Let's now calculate the ratio F/m. We have:
F = 29.4 N
m = 3.0 kg
Subsituting, we find

This is called acceleration of gravity, and it is the acceleration at which every object falls near the Earth's surface. It is indicated with the symbol
.
We can prove that this is the acceleration of the object: in fact, according to Newton's second law,

where a is the acceleration of the object. Re-arranging,

which is exactly equal to the quantity we have calculated above.
Answer:
x = 0.0537 m or 5.37 cm
Explanation:
Given:
spring constant'k'= 4900 N/m
radius 'r' =0.029 m
Area 'A' =r²π = 0.029²π => 2.6 x
m²
Here, Pressure 'P' is given by,
Pressure = Force / Area
And we know that, for a spring :
F = kx, where k is the spring constant and x is the change in length.
P = kx/A
As P = 101325 Pa
101325 = 4900x / ( 2.6 x
)
x = 0.0537 m or 5.37 cm
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