a stone of mass 200g falls from a height of 5m with a velocity of 1.5m. assuming g=10m/s, calculate the
1]potential energy
2]kinetic energy
3]velocity
just before hitting the ground
1]potential energy
p.e=mgh
m=200g, convert by dividing, 200 divided by 1000=0.2kg
g=10
h=5m
0.2kg x 10 x 5=10j
2]kinetic energy
k.e=1/2 mv2
m=0.2
v=1.5
=1/2 x 0.2 x 1.5
=1/2 x 0.2 x 2.25
=1/2 x 0.45
=0.225j
3]velocity
v=gh=1/2 v2
gh/1=v2/2
gh x2=2gh, v2 x1=v2
v2=2gh
v2=2 x 10 x 5
v2=100
v=100[square root]
v=10m/s
To calculate the potential energy, kinetic energy, and velocity of the stone just before hitting the ground, we can use the formulas of energy and motion. Here's how you can calculate each value:
1] Potential Energy (PE):
The potential energy is given by the formula: PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (given as 10 m/s²), and h is the height.
Given:
Mass (m) = 200 g = 0.2 kg
Height (h) = 5 m
Acceleration due to gravity (g) = 10 m/s²
Calculating:
PE = 0.2 kg * 10 m/s² * 5 m
PE = 10 J (Joules)
Therefore, the potential energy of the stone at a height of 5m is 10 Joules.
2] Kinetic Energy (KE):
The kinetic energy is given by the formula: KE = 0.5 * m * v^2, where m is the mass of the object and v is the velocity.
Given:
Mass (m) = 200 g = 0.2 kg
Velocity (v) = 1.5 m/s
Calculating:
KE = 0.5 * 0.2 kg * (1.5 m/s)^2
KE = 0.225 J (Joules)
Therefore, the kinetic energy of the stone with a velocity of 1.5 m/s is 0.225 Joules.
3] Velocity (v):
To calculate the velocity just before hitting the ground, we'll use the equation of motion: v² = u² + 2 * a * s, where u is the initial velocity (which is 0 as the stone is falling), a is the acceleration due to gravity (10 m/s²), and s is the distance/height.
Given:
Initial velocity (u) = 0 m/s
Acceleration due to gravity (a) = 10 m/s²
Distance/Height (s) = 5 m
Calculating:
v² = 0² + 2 * 10 m/s² * 5 m
v² = 0 + 100 m²/s² * 5 m
v² = 500 m²/s²
v ≈ 22.36 m/s (approx.)
Therefore, the velocity of the stone just before hitting the ground is approximately 22.36 m/s.