Answer:
1.324 × 10⁷ m
Explanation:
The centripetal acceleration, a at that height above the earth equal the acceleration due to gravity, g' at that height, h.
Let R be the radius of the orbit where R = RE + h, RE = radius of earth = 6.4 × 10⁶ m.
We know a = Rω² and g' = GME/R² where ω = angular speed = 2π/T where T = period of rotation = 1 day = 8.64 × 10⁴s (since the shuttle's period is synchronized with that of the Earth's rotation), G = gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², ME = mass of earth = 6 × 10²⁴ kg. Since a = g', we have
Rω² = GME/R²
R(2π/T)² = GME/R²
R³ = GME(T/2π)²
R = ∛(GME)(T/2π)²
RE + h = ∛(GMET²/4π²)
h = ∛(GMET²/4π²) - RE
substituting the values of the variables, we have
h = ∛(6.67 × 10⁻¹¹ Nm²/kg² × 6 × 10²⁴ kg × (8.64 × 10⁴s)²/4π²) - 6.4 × 10⁶ m
h = ∛(2,987,477 × 10²⁰/4π² Nm²s²/kg) - 6.4 × 10⁶ m
h = ∛75.67 × 10²⁰ m³ - 6.4 × 10⁶ m
h = ∛(7567 × 10¹⁸ m³) - 6.4 × 10⁶ m
h = 19.64 × 10⁶ m - 6.4 × 10⁶ m
h = 13.24 × 10⁶ m
h = 1.324 × 10⁷ m
Answer:
Explanation:
GIVEN
Force (F) = 8 N
Distance (d) = 2.5 metres
Work done = ?
WE know we have the formula
work done = F * d
Work done = 8 * 2.5
= 20 Joule
Hope it helps :)
Answer:
Question 1)
a) The speed of the drums is increased from 2 ft/s to 4 ft/s in 4 s. From the below kinematic equations the acceleration of the drums can be determined.

This is the linear acceleration of the drums. Since the tape does not slip on the drums, by the rule of rolling without slipping,

where α is the angular acceleration.
In order to continue this question, the radius of the drums should be given.
Let us denote the radius of the drums as R, the angular acceleration of drum B is
α = 0.5/R.
b) The distance travelled by the drums can be found by the following kinematics formula:

One revolution is equal to the circumference of the drum. So, total number of revolutions is

Question 2)
a) In a rocket propulsion question, the acceleration of the rocket can be found by the following formula:

b) 
Accelleration(a) is changing of velocity in second.
free fall a = g
speed increase = a = g = 20 (m/s) / s
Answer:
Explanation:
Let mass of cylinder be M
Moment of inertia of cylinder
= 1/2 M R² r is radius of cylinder
If radius of equivalent hoop be k
Mk² = 1/2 x MR²
k = R / √2
1.2 / 1.414
Radius of gyration = 0.848 m
b )
moment of inertia of spherical shell
= 2 / 3 M R²
Moment of inertia of equivalent hoop
Mk²
So
Mk² = 2 / 3 M R²
k = √2/3 x R
= .816 X 1.2
Radius of gyration = .98 m
c )
Moment of inertia of solid sphere
= 2/5 M R²
Moment of inertia of equivalent hoop
= Mk²
Mk² = 2/5 M R²
k √ 2/5 R
Radius of gyration = .63 R