The hoop is attached.
Consider that the friction force is given by:
F = μ·N
= μ·m·g·cosθ
We also know, considering the forces of the whole system, that:
F = -m·a + m·g·sinθ
and
a = (1/2)·<span>g·sinθ
Therefore:
</span>-(1/2)·m·g·sinθ + m·g·sinθ = <span>μ·m·g·cosθ
</span>(1/2)·m·g·sinθ = <span>μ·m·g·cosθ
</span>μ = (1/2)·m·g·sinθ / <span>m·g·cosθ
= </span>(1/2)·tanθ
Now, solve for θ:
θ = tan⁻¹(2·μ)
= tan⁻¹(2·0.9)
= 61°
Therefore, the maximum angle <span>you could ride down without worrying about skidding is
61°.</span>
Answer:
625000 N/ m
Explanation:
m= 20 kg
v= 30 m/s
x= 12 cm
k = ?
Here when the mass when hits at spring its speed is
Vi= 30 m/s
Finally it comes to rest after compressing for 12 cm
i-e Vf = 0 m/s
Distance= S= 12 cm = 0.12 m
using
2aS= Vf2 - Vi2
==> 2a ×0.12 = o- 30 × 30
==> a = 900 ÷ 0.24 = 3750 m/sec2
Now we know;
F = ma
F= -Kx
==> ma= -kx
==> 20 × 3750 = -K × 0.12
==> k = 625000 N/ m
Answer:
Explanation:
area of square loop A = side²
= 8.4² x 10⁻⁴
A = 70.56 x 10⁻⁴ m²
when it is converted into rectangle , length = 14.7 , width = 2.1
area = length x width
= 14.7 x 2.1 x 10⁻⁴
= 30.87 x 10⁻⁴ m²
Let magnetic field be B
Change in flux = magnetic field x change in area
= B x ( 70.56 x 10⁻⁴ - 30.87 x 10⁻⁴ )
= 39.69 x 10⁻⁴ B
rate of change of flux = change in flux / time taken
= 39.69 x 10⁻⁴ B / 6.5 x 10⁻³
= 6.1 x 10⁻¹ B
emf induced = 6.1 x 10⁻¹ B
6.1 x 10⁻¹ B = 14.7 ( given )
B = 2.41 x 10
= 24.1 T
B ) magnetic flux is decreasing , so it needs to be increased as per Lenz's law . Hence current induced will be anticlockwise so that additional magnetic flux is induced out of the page.
Answer:
The ratio is
Explanation:
From the question we are told that
The radius of Phobos orbit is R_2 = 9380 km
The radius of Deimos orbit is 
Generally from Kepler's third law

Here M is the mass of Mars which is constant
G is the gravitational constant
So we see that 
=> ![[\frac{T_1}{T_2} ]^2 = [\frac{R_1}{R_2} ]^3](https://tex.z-dn.net/?f=%5B%5Cfrac%7BT_1%7D%7BT_2%7D%20%5D%5E2%20%3D%20%20%5B%5Cfrac%7BR_1%7D%7BR_2%7D%20%5D%5E3)
Here
is the period of Deimos
and
is the period of Phobos
So
![[\frac{T_1}{T_2} ] = [\frac{R_1}{R_2} ]^{\frac{3}{2}}](https://tex.z-dn.net/?f=%5B%5Cfrac%7BT_1%7D%7BT_2%7D%20%5D%20%3D%20%20%5B%5Cfrac%7BR_1%7D%7BR_2%7D%20%5D%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D)
=> ![\frac{T_1}{T_2} = [\frac{23500 }{9380} ]^{\frac{3}{2}}]](https://tex.z-dn.net/?f=%5Cfrac%7BT_1%7D%7BT_2%7D%20%20%3D%20%20%5B%5Cfrac%7B23500%20%7D%7B9380%7D%20%5D%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%5D)
=>