A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling hori
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<h2>Answer:</h2>
Torque = <em>2.05 x 10²⁸ Nm</em>
Energy = <em>3.54 x 10³³ J</em>
Average power = <em>1.02 x 10²⁸ W</em>
<h2>Explanation:</h2>(a) Torque (τ) is the rotational effect of a given force.
It is given by
τ = I x α -------------(i)
Where;
I = rotational inertia of the object
α = angular acceleration of the object.
In this case, the object is the Earth. Therefore,
I = 9.71 x 10³⁷ kg m²
α = ω / t
Where;
ω = angular velocity of earth = 2π rad / day
<em>Since </em>
<em>1 day = 24 hours and 1 hour = 3600seconds</em>
<em>1 day = 24 x 3600 seconds = 86400seconds</em>
<em>=> ω = 2π rad / 86400seconds</em>
<em>=> ω = 7.29 × 10⁻⁵ rad/s</em>
<em />
t = 4 days = 4 x 24 x 3600 seconds = 345600 seconds
=> α = ω / t
=> α = 7.29 × 10⁻⁵ / 345600
=> α = (7.29 × 10⁻⁵) / (3.456 x 10⁵)
=> α = (7.29 × 10⁻⁵⁻⁵) / (3.456)
=> α = (7.29 × 10⁻¹⁰) / (3.456)
=> α = 2.11 × 10⁻¹⁰ rad/s²
Now substitute the values of I and α into equation (i)
τ = 9.71 x 10³⁷ x 2.11 × 10⁻¹⁰
τ = 9.71 x 10²⁷ x 2.11
τ = 20.5 x 10²⁷ Nm
τ = 2.05 x 10²⁸ Nm
(ii) The energy (rotational energy) E is given by;
E = x I x ω
E = x 9.71 x 10³⁷ x 7.29 × 10⁻⁵
E = 35.4 x 10³² J
E = 3.54 x 10³³ J
(iii) The average power P, is given by;
P = E / t
P = 3.54 x 10³³ / 345600
P = 1.02 x 10²⁸ W
Answer:
Speed will be equal to 1.40 m/sec
Explanation:
Mass of the rubber ball m = 5.24 kg = 0.00524 kg
Spring is compressed by 5.01 cm
So x = 5.01 cm = 0.0501 m
Spring constant k = 8.08 N/m
Frictional force f = 0.031 N
Distance moved by ball d = 15.8 cm = 0.158 m
Energy gained by spring
Energy lost due to friction
So remained energy to move the ball = 0.0101 - 0.0048 = 0.0052 J
This energy will be kinetic energy
v = 1.40 m/sec