a body of mass 5kg falls vertically against a resistance of x Newtons.The body passes through two points A and B, 2.5 METERS APART with A above B, WHEN TRAVELING WITH SPEED 2 METERS PER SECOND AND 6 METERS PER SECOND RESPECTIVELY. BY ENERGY CONSIDERATION , FIND THE VALUE OF X.
To find the value of x (the resistance force), we can use the principle of conservation of energy.
The initial energy of the body at point A can be calculated using the formula for gravitational potential energy:
E_initial = m * g * h
where
m = mass of the body (5 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height difference between points A and B (unknown)
The final energy of the body at point B can be calculated by combining the work done against the resistance force with the kinetic energy of the body:
E_final = work done against resistance + kinetic energy
The work done against the resistance force can be calculated using the formula:
Work = force * distance
where
force = the resistance force (x Newtons)
distance = distance between points A and B (2.5 meters)
The kinetic energy of the body at point B can be calculated using the formula:
Kinetic energy = 0.5 * m * v^2
where
v = velocity of the body at point B (6 m/s)
Since energy is conserved, we can equate the initial energy to the final energy:
E_initial = E_final
m * g * h = force * distance + 0.5 * m * v^2
Substituting the known values, we get:
5 kg * 9.8 m/s^2 * h = x N * 2.5 m + 0.5 * 5 kg * (6 m/s)^2
49 h = 2.5x + 90
Now, we can solve the equation to find the value of x.
Note: The equation relates the unknown height difference (h) and resistance force (x). The values provided for speed (2 m/s and 6 m/s) are used to calculate the kinetic energy at point B.