A 5.36 kg object falls freely (ignore air resistance), after being dropped from rest. Determine the initial kinetic energy, the final kinetic energy, and the change in kinetic energy for the following.
(a) first meter of fall
initial kinetic energy 0 J
final kinetic energy ___ J
(b) second meter of fall
initial kinetic energy ___ J
final kinetic energy ___ J
m*g = 5.36k * 9.8N/kg = 52.53 N. = Wt.
of object.
a. KE = 0 J. = Initial KE
V^2 = Vo^2 + 2g*h
V^2 = 0 + 19.6*1 = 19.6
V = 4.43 m/s.
KE = 0.5m*V^2 = 2.68*4.43^2 = 52.59 J.
b. V^2 = Vo^2 + 2g*h
V^2 = 4.43^2 + 19.6*1 = 39.22
V = 6.26 m/s.
KEo = 2.68*4.43^2 = 52.59 J.
KE = 2.68*6.26^2 = 105 J.
(a)
Initial kinetic energy: 0 J
Final kinetic energy: Well, let's calculate that using the formula for kinetic energy, which is 1/2 * mass * velocity squared. Since the object falls freely, its initial velocity is 0 m/s. So the final kinetic energy would still be 0 J. Ain't that an electrifying outcome?
(b)
Initial kinetic energy: Since the object has fallen one meter already, its initial velocity would be the square root of 2 times the acceleration due to gravity (g), which is approximately 9.8 m/s². Plugging in the values, we get: 1/2 * 5.36 kg * (9.8 m/s)² = 254.696 J (rounding to three decimal places for extra clown accuracy).
Final kinetic energy: For the second meter of fall, we need to calculate the velocity at that height. Using the equation v^2 = u^2 + 2as (where u is the initial velocity, a is the acceleration, and s is the distance), we can find that the final velocity at the end of the second meter would be approximately 13.86 m/s. Plugging this value into the kinetic energy formula, we get: 1/2 * 5.36 kg * (13.86 m/s)² = 506.313 J (rounding again).
Change in kinetic energy: To find the change in kinetic energy, we subtract the initial kinetic energy from the final kinetic energy. So, the change in kinetic energy would be 506.313 J - 0 J which equals an extravagant 506.313 J. That's quite a jump in energy, isn't it?
To determine the initial kinetic energy, final kinetic energy, and change in kinetic energy for an object falling freely, we need to use the equations for kinetic energy.
The formula for kinetic energy is:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
(a) For the first meter of fall:
- The initial kinetic energy is 0 J. This is because the object starts from rest, so its initial velocity is zero. Plugging this value into the kinetic energy equation, we get:
KE_initial = (1/2) * 5.36 kg * (0 m/s)^2
KE_initial = 0 J
- To determine the final kinetic energy, we need to calculate the velocity of the object at the end of the first meter of fall. Since the object is freely falling, it experiences constant acceleration due to gravity (9.8 m/s^2). Using the equation for velocity:
v_final = sqrt(2 * acceleration * distance)
v_final = sqrt(2 * 9.8 m/s^2 * 1 m)
v_final ≈ 4.427 m/s
Now, we can calculate the final kinetic energy:
KE_final = (1/2) * 5.36 kg * (4.427 m/s)^2
KE_final ≈ 52.22 J
- The change in kinetic energy is then the difference between the final and initial kinetic energy:
Change in KE = KE_final - KE_initial
Change in KE = 52.22 J - 0 J
Change in KE ≈ 52.22 J
(b) For the second meter of fall:
- The initial kinetic energy can be calculated using the final velocity from the first part as the initial velocity for the second part. The final velocity after the first meter of fall is 4.427 m/s. Plugging this value into the kinetic energy equation, we get:
KE_initial = (1/2) * 5.36 kg * (4.427 m/s)^2
KE_initial ≈ 51.88 J
- Similarly, to determine the final kinetic energy, we need to calculate the velocity of the object at the end of the second meter of fall. Using the equation for velocity:
v_final = sqrt(2 * acceleration * distance)
v_final = sqrt(2 * 9.8 m/s^2 * 1 m)
v_final ≈ 6.26 m/s
Now, we can calculate the final kinetic energy:
KE_final = (1/2) * 5.36 kg * (6.26 m/s)^2
KE_final ≈ 99.23 J
- The change in kinetic energy is then the difference between the final and initial kinetic energy:
Change in KE = KE_final - KE_initial
Change in KE = 99.23 J - 51.88 J
Change in KE ≈ 47.35 J
To determine the initial and final kinetic energy and the change in kinetic energy for each meter of fall, we need to use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the object is in free fall with no air resistance, we can use the equation for velocity in free fall:
Velocity = √(2 * gravitational acceleration * height)
The gravitational acceleration, usually denoted as "g," is approximately equal to 9.8 m/s^2 on Earth.
Now let's calculate the values for each part:
(a) First meter of fall:
The height is 1 meter.
To find the initial kinetic energy, we substitute the initial velocity as 0 m/s into the kinetic energy formula:
Initial kinetic energy = (1/2) * mass * initial velocity^2 = (1/2) * 5.36 kg * 0 m/s = 0 J.
To find the final kinetic energy, we substitute the velocity at 1 meter height into the kinetic energy formula:
Final velocity = √(2 * 9.8 m/s^2 * 1 m) = √19.6 m^2/s^2 ≈ 4.43 m/s.
Final kinetic energy = (1/2) * mass * final velocity^2 = (1/2) * 5.36 kg * (4.43 m/s)^2 = 52.96 J.
The change in kinetic energy is the difference between the final and initial kinetic energy:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy = 52.96 J - 0 J = 52.96 J.
Therefore, the answers for the first meter of fall are:
Initial kinetic energy = 0 J.
Final kinetic energy = 52.96 J.
Change in kinetic energy = 52.96 J.
(b) Second meter of fall:
The height is 2 meters.
To find the initial kinetic energy, we substitute the final velocity of the previous part, 4.43 m/s, into the kinetic energy formula:
Initial kinetic energy = (1/2) * mass * initial velocity^2 = (1/2) * 5.36 kg * (4.43 m/s)^2 ≈ 49.24 J.
To find the final kinetic energy, we substitute the velocity at 2 meters height into the kinetic energy formula:
Final velocity = √(2 * 9.8 m/s^2 * 2 m) = √39.2 m^2/s^2 ≈ 6.26 m/s.
Final kinetic energy = (1/2) * mass * final velocity^2 = (1/2) * 5.36 kg * (6.26 m/s)^2 ≈ 98.34 J.
The change in kinetic energy is the difference between the final and initial kinetic energy:
Change in kinetic energy = Final kinetic energy - Initial kinetic energy = 98.34 J - 49.24 J ≈ 49.10 J.
Therefore, the answers for the second meter of fall are:
Initial kinetic energy ≈ 49.24 J.
Final kinetic energy ≈ 98.34 J.
Change in kinetic energy ≈ 49.10 J.