The final velocity is 5.87 m/s
<u>Explanation:</u>
Given-
mass, = 72 kg
speed, = 5.8 m/s
,
= 45 kg
,
= 12 m/s
Θ = 60°
Final velocity, v = ?
Applying the conservation of momentum:
X
+
X
= (
+
) v
72 X 5.8 + 45 X 12 X cos 60° = (72 + 45) v
v = 417.6 + 540 X
v = 417.6 +
v = 5.87 m/s
The final velocity is 5.87 m/s
To solve this problem it is necessary to apply the kinematic equations of angular motion.
Torque from the rotational movement is defined as
where
I = Moment of inertia For a disk
Angular acceleration
The angular acceleration at the same time can be defined as function of angular velocity and angular displacement (Without considering time) through the expression:
Where
Final and Initial Angular velocity
Angular acceleration
Angular displacement
Our values are given as
Using the expression of angular acceleration we can find the to then find the torque, that is,
With the expression of the acceleration found it is now necessary to replace it on the torque equation and the respective moment of inertia for the disk, so
Therefore the torque exerted on it is