Answer:
v = 8.96 m/s
Explanation:
Initial speed of the ball, u = 10 m/s
It caught 1 meter above its initial position.
Acceleration due to gravity,
We need to find the final speed of the ball when it is caught. Let is equal to v. To find the value of v, use third equation of motion as :
v = 8.96 m/s
So, the speed of the ball when it is caught is 8.96 m/s. Hence, this is the required solution.
Answer:
<em>a) 0.67 rad/sec in the clockwise direction.</em>
<em>b) 98.8% of the kinetic energy is lost.</em>
Explanation:
Let us take clockwise angular speed as +ve
For first cylinder
rotational inertia = 2.0 kg-m^2
angular speed ω = +5.0 rad/s
For second cylinder
rotational inertia = 1.0 kg-m^2
angular speed = -8.0 rad/s
The rotational momentum of a rotating body is given as = ω
where is the rotational inertia
ω is the angular speed
The rotational momenta of the cylinders are:
for first cylinder = ω = 2.0 x 5.0 = 10 kg-m^2 rad/s
for second cylinder = ω = 1.0 x (-8.0) = -8 kg-m^2 rad/s
The total initial angular momentum of this system cylinders before they were coupled together = 10 + (-8) = <em>2 kg-m^2 rad/s</em>
When they are coupled coupled together, their total rotational inertia = 1.0 + 2.0 = 3 kg-m^2
Their final angular rotational momentum after coupling =
where is their total rotational inertia
= their final angular speed together
Final angular momentum = 3 x = 3
According to the conservation of angular momentum, the initial rotational momentum must be equal to the final rotational momentum
this means that
2 = 3
= final total angular speed of the coupled cylinders = 2/3 = <em>0.67 rad/s</em>
From the first statement, <em>the direction is clockwise</em>
b) Rotational kinetic energy =
where is the rotational inertia
is the angular speed
The kinetic energy of the cylinders are:
for first cylinder = =
= 25 J
for second cylinder = = 32 J
Total initial energy of the system = 25 + 32 = 57 J
The final kinetic energy of the cylinders after coupling =
where
where is the total rotational inertia of the cylinders
is final total angular speed of the coupled cylinders
Final kinetic energy = = 0.67 J
kinetic energy lost = 57 - 0.67 = 56.33 J
percentage = 56.33/57 x 100% = <em>98.8%</em>