Explanation:
The free fall acceleration is:
F = ma
20 N = (0.50 kg) a
a = 40 m/s²
The mass of Planet X is:
F = GMm / r²
20 N = (6.67×10⁻¹¹ Nm²/kg²) M (0.50 kg) / (4.0×10⁶ m)²
M = 9.6×10²⁴ kg
Answer:
1. T₁ = 500 N
2. T₂ = 866 N
Explanation:
Please see attached photo for the diagram.
Thus, we can obtain obtained the value of T₁ and T₂ as follow:
1. Determination of T₁
Angle θ = 30
Hypothenus = 100 kg
Opposite = T₁ =?
Sine θ = Opposite /Hypothenus
Sine 30 = T₁ / 100
Cross multiply
T₁ = 100 × Sine 30
T₁ = 100 × 0.5
T₁ = 50 Kg
Multiply by 10 to express in Newton
T₁ = 50 × 10
T₁ = 500 N
2. Determination of T₂
Angle θ = 60
Hypothenus = 100 kg
Opposite = T₂ = ?
Sine θ = Opposite /Hypothenus
Sine 60 = T₂ / 100
Cross multiply
T₂ = 100 × Sine 60
T₂ = 100 × 0.8660
T₂ = 86.6 Kg
Multiply by 10 to express in Newton
T₂ = 86.6 × 10
T₂ = 866 N
Answer:
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
Given data
mass = 3 slugs = 3 * 32.14 = 96.52 lbs
constant k = 9 lbs/ft
Beta = 6lbs * s/ft
mass is pulled = 1 ft below
to find out
equation of motion for the mass
solution
we know that The mass is pulled 1 ft below so
we will apply here differential equation of free motion i.e
dx²/dt² + 2 α dx/dt + ω² x =0 ........................1
here 2 α = Beta / mass
so 2 α = 6 / 96.52
α = 0.031
α² = 0.000961 ...............2
and
ω² = k/mass
ω² = 9 /96.52
ω² = 0.093 ..................3
we can say that from equation 2 and 3 that α² - ω² = -0.092239
this is less than zero
so differential equation is
x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
The same thing happened in pressure cooker but the temperature inside is most higher.
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Here we know that mass of the person is 90 kg
His weight is given as 30 lbf
so here we can convert it into Newton as we know that
1 lbf = 4.45 N
Now from above conversion
now we can use this to find the gravity at this height
now we know that with height gravity varies as
so above is the height from the surface of earth
