What is the decrease in elevation of a 4-kg body whose kinetic energy increases from 20 J to 100 J as a result of moving downward along an inclined plane?
set Potential energy change equal to KE change
mgh= change in KE
thanks a lot!
change in W = 100J-20J
mgh = 80J
40(9.8)(d) = 80J
39.2(d) = 80J
d = 2.040816327m.
Well, let me put on my mathematician clown hat for this one! *Honk, honk!* Okay, let's calculate this together.
We have a 4-kg body moving downward along an inclined plane. The change in kinetic energy is from 20 J to 100 J. We want to find the decrease in elevation, which is equivalent to the change in potential energy.
Now, potential energy is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the change in elevation.
We know that change in kinetic energy is equal to the change in potential energy. So, we can set up the equation as follows:
mgh = change in KE
Substituting the given values:
4 kg * 9.8 m/s² * h = 100 J - 20 J
Simplifying that equation will give us the value of h, the decrease in elevation. *Honk, honk!*
You're welcome! Let's calculate the decrease in elevation using the equation you mentioned, where the change in potential energy is equal to the change in kinetic energy.
We can start by rearranging the equation to solve for the change in height (Δh):
mgh = ΔKE
Δh = ΔKE / (mg)
Now we can substitute the given values into the equation:
m = 4 kg
ΔKE = 100 J - 20 J = 80 J
g = 9.8 m/s² (acceleration due to gravity)
Δh = (80 J) / (4 kg * 9.8 m/s²)
Simplifying the equation:
Δh = 80 J / 39.2 N
Calculating:
Δh ≈ 2.04 meters
Therefore, the body will decrease its elevation by approximately 2.04 meters as it moves downward along the inclined plane.
You're welcome! To find the decrease in elevation, we can use the equation relating potential energy, kinetic energy, mass, and height. It states that the potential energy change is equal to the change in kinetic energy.
To solve for the decrease in elevation, we plug in the values we have into the equation:
mgh = change in KE
Here, m represents the mass of the body (4 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), h stands for the decrease in elevation that we want to find, and change in KE is the difference in kinetic energy (100 J - 20 J = 80 J).
Substituting the given values into the equation gives:
4 kg × 9.8 m/s^2 × h = 80 J
We can simplify further by dividing both sides of the equation by (4 kg × 9.8 m/s^2):
h = 80 J ÷ (4 kg × 9.8 m/s^2)
Evaluating this expression gives:
h = 2 m
Therefore, the decrease in elevation of the 4-kg body is 2 meters.