A) Use the principle of conservation of energy to calculate the maximum height reached by a projectile shot straight up from ground level with a speed of 120.0 m/s
B)
What real force (a manifestation of one of the fundamental four forces) would cause the actual maximum height to be less than the height of part (a) one or two words are sufficient.
A) To calculate the maximum height reached by a projectile shot straight up, we can use the principle of conservation of energy. The projectile will initially have kinetic energy due to its motion, which will then be converted into gravitational potential energy at its highest point. At this point, all of the projectile's initial kinetic energy will be transformed into potential energy.
To begin, we need to determine the initial kinetic energy of the projectile. The kinetic energy of an object is given by the formula:
KE = (1/2) * m * v^2
Where KE represents kinetic energy, m is the mass of the object, and v is the velocity.
In this case, the projectile's initial velocity is given as 120.0 m/s. We don't have the mass of the projectile, but it cancels out when we calculate the ratio between potential and kinetic energy. Therefore, we can ignore the mass for this calculation.
Next, we calculate the potential energy of the projectile at its maximum height using the formula:
PE = m * g * h
Where PE represents potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
Since we're interested in the maximum height, we want to find h in terms of the given initial velocity. At its highest point, the projectile's final velocity will be 0 m/s. Using the equation of motion v^2 = u^2 + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement, we can find the displacement (maximum height) as:
0^2 = (120.0)^2 + 2 * (-9.8) * h
Simplifying the equation, we get:
0 = (120.0)^2 - 19.6h
Rearranging the equation and solving for h, we find:
h = (120.0)^2 / 19.6
Evaluating this expression gives us the maximum height reached by the projectile.
B) The real force that would cause the actual maximum height to be less than the height calculated in part (a) is air resistance. Air resistance opposes the motion of the projectile and will cause it to lose energy as it moves upward. The impact of air resistance depends on various factors such as the shape and size of the projectile, the density of the air, and the velocity of the projectile. Therefore, in the real world, the maximum height reached by the projectile will generally be less than the calculated theoretical maximum height due to the presence of air resistance.