Answer:
The speed of the block is 8.2 m/s
Explanation:
Given;
mass of block, m = 2.1 kg
height above the top of the spring, h = 5.5 m
First, we determine the spring constant based on the principle of conservation of potential energy
¹/₂Kx² = mg(h +x)
¹/₂K(0.25)² = 2.1 x 9.8(5.5 +0.25)
0.03125K = 118.335
K = 118.335 / 0.03125
K = 3786.72 N/m
Total energy stored in the block at rest is only potential energy given as:
E = U = mgh
U = 2.1 x 9.8 x 5.5 = 113.19 J
Work done in compressing the spring to 15.0 cm:
W = ¹/₂Kx² = ¹/₂ (3786.72)(0.15)² = 42.6 J
This is equal to elastic potential energy stored in the spring,
Then, kinetic energy of the spring is given as:
K.E = E - W
K.E = 113.19 J - 42.6 J
K.E = 70.59 J
To determine the speed of the block due to this energy:
KE = ¹/₂mv²
70.59 = ¹/₂ x 2.1 x v²
70.59 = 1.05v²
v² = 70.59 / 1.05
v² = 67.229
v = √67.229
v = 8.2 m/s
Answer:
Kinetic energy of the system = 2547.41 Joules.
Explanation:
Given:
Disk:
Mass of the disk (m) =
kg
Radius of the disk (r) =
cm =
m
Cylinder:
Mass of the annular cylinder (M) =
kg
Inner radius of the cylinder
=
m
Outer radius of the cylinder
=
m
The angular speed of the system
=
rev/s
Angular speed in in terms of Rad/sec =
rad/sec
Formula to be used:
Rotational Kinetic energy,
= 
So, before that we have to work with the moment of inertia (MOI) of the system.
⇒ MOI of the system = MOI of the disk + MOI of the cylinder
⇒ MOI (system) = 
⇒ MOI (system) = 
⇒ MOI (system) =
kg.m^2
Now
The rotational Kinetic energy.
⇒ 
Plugging the values.
⇒ 
⇒
Joules
Then
The kinetic energy of the rotational system is 2547.41 J.
Answer:
They will run parallel to each other as the none of a straight pole cannot be bent in such a way where one side can turn without the other turning.