A ball having a weight of 1.5 N is dropped from a height of 4 meters. (Neglect air friction.) How much mechanical energy is "lost" just before it hits the ground?
M*g = 1.5, M = 1.5/g = 1.5/9.8 = 0.153 kg.
PE = Mg*h = 1.5 * 4 = 6.0 J.
V^2 = Vo^2 + 2g*h = 0 + 19.6*4 = 78.4 (m/s)^2.
KE = 0.5M*V^2 = 0.5*0.153*78.4 = 6.0 Joules.
Energy Lost = PE - KE = 6-6 = 0.
To calculate the mechanical energy lost by the ball just before it hits the ground, we need to determine the potential energy it had at the initial height and the kinetic energy it has just before hitting the ground.
Step 1: Calculate the potential energy:
Potential energy (PE) = mass * gravity * height
Given:
Weight of the ball = 1.5 N (weight = mass * gravity)
Height = 4 meters
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Since weight = mass * gravity, we can rearrange the formula to find mass:
mass = weight / gravity
mass = 1.5 N / 9.8 m/s^2 ≈ 0.153 kg
Now, we can calculate the potential energy:
PE = mass * gravity * height
PE = 0.153 kg * 9.8 m/s^2 * 4 m
PE = 5.9964 J (approximately)
Step 2: Calculate the kinetic energy:
At the moment just before the ball hits the ground, all its potential energy would have been converted into kinetic energy.
Therefore, the kinetic energy is equal to the potential energy.
Kinetic energy (KE) = 5.9964 J (from Step 1)
Step 3: Calculate the mechanical energy lost:
Since mechanical energy is conserved in the absence of air friction, the mechanical energy lost is equal to the difference between the potential energy and kinetic energy.
Mechanical energy lost = PE - KE
Mechanical energy lost = 5.9964 J - 5.9964 J
Mechanical energy lost = 0 J
Therefore, no mechanical energy is "lost" just before the ball hits the ground as it is converted entirely into kinetic energy.
To determine how much mechanical energy is "lost" just before the ball hits the ground, we need to calculate the initial mechanical energy and the final mechanical energy of the ball.
Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE).
Given:
Weight of the ball = 1.5 N
Height from which it is dropped = 4 meters
Step 1: Calculate the initial mechanical energy (Ei) of the ball.
Since the ball is dropped from rest, the initial kinetic energy (KEi) is zero.
The initial potential energy (PEi) can be calculated using the formula:
PEi = m * g * h
where:
m = mass of the ball (unknown)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height = 4 meters
Since weight is given by the formula:
Weight = m * g
where:
m = mass
g = acceleration due to gravity
We can rearrange the formula to find the mass (m), which is:
m = Weight / g
Substituting the given values:
m = 1.5 N / 9.8 m/s^2 (approximation for g)
Calculate the mass (m) using the given weight of the ball.
Step 2: Calculate the final mechanical energy (Ef) of the ball.
When the ball is about to hit the ground, its height is zero. So, the final potential energy (PEf) will be zero.
To calculate the final kinetic energy (KEf), we can use the equation:
KEf = (1/2) * m * v^2
where:
m = mass (calculated in Step 1)
v = velocity of the ball just before hitting the ground (unknown)
Since the ball is dropped from rest, it falls freely under the influence of gravity. We can use the equation for the final velocity (v) of an object in free fall:
v = sqrt(2 * g * h)
where:
g = acceleration due to gravity
h = height = 4 meters
Substitute the given values into the equation to find the final velocity (v) of the ball.
Step 3: Calculate the mechanical energy lost (ΔE).
The mechanical energy lost can be determined by subtracting the final mechanical energy (Ef) from the initial mechanical energy (Ei):
ΔE = Ei - Ef
Calculate ΔE using the calculated initial and final mechanical energy.
This process will give you the amount of mechanical energy "lost" just before the ball hits the ground.