Answer:
(A) 0.63 J
(B) 0.15 m
Explanation:
length (L) = 0.75 m
mass (m) =0.42 kg
angular speed (ω) = 4 rad/s
To solve the questions (a) and (b) we first need to calculate the rotational inertia of the rod (I)
I = Ic + m
Ic is the rotational inertia of the rod about an axis passing trough its centre of mass and parallel to the rotational axis
h is the horizontal distance between the center of mass and the rotational axis of the rod
I = ![(\frac{1}{12})(mL^{2} ) + m([tex]\frac{L}{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B12%7D%29%28mL%5E%7B2%7D%20%29%20%2B%20m%28%5Btex%5D%5Cfrac%7BL%7D%7B2%7D)
)^{2}[/tex]
I = ![(\frac{1}{12})(0.42 x 0.75^{2} ) + ( 0.42 x ([tex]\frac{0.75}{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B12%7D%29%280.42%20x%200.75%5E%7B2%7D%20%29%20%2B%20%28%200.42%20x%20%28%5Btex%5D%5Cfrac%7B0.75%7D%7B2%7D)
)^{2}[/tex])
I = 0.07875 kg.m^{2}
(A) rods kinetic energy = 0.5I
= 0.5 x 0.07875 x 
= 0.63 J 0.15 m
(B) from the conservation of energy
initial kinetic energy + initial potential energy = final kinetic energy + final potential energy
Ki + Ui = Kf + Uf
at the maximum height velocity = 0 therefore final kinetic energy = 0
Ki + Ui = Uf
Ki = Uf - Ui
Ki = mg(H-h)
where (H-h) = rise in the center of mass
0.63 = 0.42 x 9.8 x (H-h)
(H-h) = 0.15 m
Given that
Velocity of missile (v) = 20 m/s ,
Angle of missile (Θ) = 53°
Determine , Vertical component = v sin Θ
= 20 sin 53°
= 15.97 m/s
When you're talking about gravity, it's easy to identify the equal
opposite forces.
Gravity ALWAYS produces an equal pair of opposite forces.
They both act between the centers of the two objects, one in
each direction.
Consider the equal pair of opposite gravitational forces between
you and the Earth. One force acts on you, and draws you toward
the center of the Earth. We call that force "your weight".
The other one acts on the Earth, and draws it toward the center
of you. Hardly anybody ever talks about that one, but the two
forces are equal ... your weight on Earth is equal to the Earth's
weight on you !
Answer:
Explanation:
We shall show all given data in vector form and calculate the direction of force with the help of following formula
force F = q ( v x B )
q is charge , v is velocity and B is magnetic field.
Given B = - Bk ( i is right , j is upwards and k is straight up the page )
v = v j
F = q ( vj x - Bk )
= -Bqvi
The direction is towards left .
a ) If velocity is down
v = - v j
F = q ( - vj x - bk )
= qvB i
Direction is right .
b ) v = v i
F = q ( vi x - Bk )
= qvB j
force is upwards
c ) v = - vi
F = q ( -vi x - Bk )
= -qvBj
force is downwards
d ) v = - v k
F = q( - vk x -Bk )
= 0
No force will be created
e ) v = v k
F = q( vk x -Bk )
= 0
No force will be created
The hardest part of the job is to find the right formula to use, and write it down. You've already done that ! The rest is just turning the crank until an answer falls out.
You wrote. E = m g h.
Beautiful.
Now divide each side by (g h), and you'll have the formula for mass:
m = E / (g h).
You know all the numbers on the right side. Just pluggum in, do the arithmetic, and you'll have the mass.
