The ratio of the kinetic energy of the block/bullet system immediately after the collision to the initial kinetic energy of the bullet is 0.78 %.
<h3>Final velocity of the block/bullet system</h3>
Apply the principle of conservation of energy to determine the final velocity of the block/bullet system.
K.E = P.E
¹/₂mv² = mgh
¹/₂v² = gh
v² = 2gh
v = √2gh
where;
- h is the maximum height reached by the system
- v is the initial velocity of the system
v = √(2 x 9.8 x 1.1)
v = 4.64 m/s
<h3>Initial velocity of the bullet</h3>
Apply the principle of conservation of linear momentum.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
- u₁ is the initial velocity of the bullet
- u₂ is the initial velocity of the block
- v is the final velocity after collision
- m₁ is mass bullet
- m₂ is mass of block
(0.0075)u₁ + (0.95)(0) = 4.64(0.0075 + 0.95)
0.0075u₁ = 4.4428
u₁ = 4.4428/0.0075
u₁ = 592.37 m/s
<h3>Initial kinetic energy of the bullet</h3>
K.Ei = ¹/₂m₁u₁²
K.Ei = ¹/₂(0.0075)(592.37)²
K.Ei = 1,315.88 J
<h3>Final kinetic energy of the block/bullet system</h3>
K.Ef = ¹/₂(m₁ + m₂)v²
K.Ef = ¹/₂(0.0075 + 0.95)(4.64)²
K.Ef = 10.31 J
<h3>Ratio of final kinetic energy to initial kinetic energy</h3>
= K.Ef/K.Ei x 100%
= (10.31 / 1,315.88) x 100%
= 0.78 %
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Answer:
D potential energy at the top of the stairs, kinetic energy as she walks down
Explanation:
The potential energy of a body is the energy due to the position of the body.
At the top of the stair case, the student is at a significant height.
Kinetic energy is the energy due to the motion of the body.
As the student descends, the potential energy is changed to kinetic energy.
To find the potential energy;
P.E = mgH
m is the mass
g is the acceleration due to gravity
H is the height of the body
To find the kinetic energy;
K.E = 
m v²
m is the mass
v is the velocity
Answer:
X=m*g/K
Explanation:
Since the elastic force of the spring is balancing the force of gravity:
Fe = m*g
Now, on the spring by Hook's law, the magnitude of the elastic force will be:
Fe = K*X where K is the elastic constant of the spring and X is the distance the spring is strectches measured from its original lenght to its current length.
Replacing this value:
K*X = m*g Solving for X:
X = m*g/K This value is directly proportional to the object's weight and inversely proportional to the spring's constant.
