Respuesta :
Answer:
The velocity of the bucket is 3.83 m/s.
Explanation:
Given that,
Mass of bucket = 2.0 kg
Mass of cylinder =4.0 kg
Distance = 1.50 m
We need to calculate the speed
Using equation of motion
[tex]v^2=u^2+2as[/tex]
Put the value into the formula
[tex]v^2=2\times a\times1.50[/tex]
[tex]v=\sqrt{2\times a\times1.50}[/tex]
We need to calculate the tension
Using equilibrium equation
[tex]mg=T+ma[/tex]
[tex]T=m(g-a)[/tex]....(I)
Put the value into the formula
[tex]T=2.0\times(9.8-a)[/tex]
Now, using formula of tension
[tex]T=I\\omega[/tex]...(II)
Moment of inertia of cylinder
[tex]I=\dfrac{1}{2}MR^2[/tex]
Angular velocity of cylinder is
[tex]\omega=\dfrac{a}{R^2}[/tex]
Put the value of angular velocity in equation (II)
[tex]T=\dfrac{1}{2}M\times(\dfrac{a}{\omega})\times\omega[/tex]
[tex]T=\dfrac{1}{2}M\times a[/tex]
Put the value of tension in equation (I)
[tex]\dfrac{1}{2}M\times a=m(g-a)[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}\times4.0\times a=2.0(9.8-a)[/tex]
[tex]a=\dfrac{2.0\times9.8}{4.0}[/tex]
[tex]a=4.9\ m/s^2[/tex]
Put the value of acceleration in equation of motion
[tex]v^2=2\times4.9\times1.50[/tex]
[tex]v=\sqrt{2\times4.9\times1.50}[/tex]
[tex]v=3.83\ m/s[/tex]
Hence, The velocity of the bucket is 3.83 m/s.
Answer:
Explanation:
Given mass of bucket is [tex]m=2\ kg[/tex]
mass of cylinder [tex]M=4\ kg[/tex]
Suppose T is the tension in the rope
For bucket [tex]mg-T=ma[/tex]
where a=acceleration
For cylinder with Radius R
[tex]I\times \alpha =T\cdot R[/tex]
[tex]\frac{MR^2}{2}\times \frac{a}{R}=T\times R[/tex]
[tex]T=\frac{Ma}{2}[/tex]
[tex]a=\frac{mg}{m+0.5M}[/tex]
[tex]a=4.9\ m/s^2[/tex]
Using [tex]v^2-u^2=2a s[/tex] for bucket
v=final velocity
u=initial velocity
s=displacement
[tex]v^2-0=2\times 4.9\times 1.5[/tex]
[tex]v=\sqrt{14.7}[/tex]
[tex]v=3.83\ m/s[/tex]
