As a block of wood with the mass of 2.00 kg slides along a floor, it's speed decreases from 4.0 m/s to 1.0 m/s. How much kinetic energy does it lose?
Kinetic energy is defined with
K = 1/2*m*v^2
so you have Kf - Ki
[1/2(m)(vf)^2] - [1/2(m)(vi)^2] =
m = mass
v = velocity; f for final, i for initial
your answer will be in kg * m/s^2
which is the developed way of writing Newtons because 1 kg * m/s^2 = 1 N
To calculate the amount of kinetic energy lost by the block of wood, we need to find the difference between the initial and final kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass (m) = 2.00 kg
Initial velocity (v_i) = 4.0 m/s
Final velocity (v_f) = 1.0 m/s
First, we'll find the initial kinetic energy (KE_i):
KE_i = (1/2) * m * v_i^2
Substituting the given values:
KE_i = (1/2) * 2.00 kg * (4.0 m/s)^2
KE_i = (1/2) * 2.00 kg * 16.0 m^2/s^2
KE_i = 16.00 kg.m^2/s^2
Next, we'll find the final kinetic energy (KE_f):
KE_f = (1/2) * m * v_f^2
Substituting the given values:
KE_f = (1/2) * 2.00 kg * (1.0 m/s)^2
KE_f = (1/2) * 2.00 kg * 1.0 m^2/s^2
KE_f = 1.00 kg.m^2/s^2
Now, we can find the difference between the initial and final kinetic energy to determine how much kinetic energy was lost:
Kinetic Energy Lost = KE_i - KE_f
Kinetic Energy Lost = 16.00 kg.m^2/s^2 - 1.00 kg.m^2/s^2
Kinetic Energy Lost = 15.00 kg.m^2/s^2
Therefore, the block of wood loses 15.00 kg.m^2/s^2 of kinetic energy.