A projectile of mass 0.650 kg is shot straight up with an initial speed of 20.0 m/s.
If the projectile rises to a maximum height of only 12.4 m, determine the magnitude of the average force due to air resistance.
To determine the magnitude of the average force due to air resistance, we need to analyze the motion of the projectile.
First, we can determine the initial kinetic energy of the projectile using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the projectile is 0.650 kg and the initial speed is 20.0 m/s, we can calculate the initial kinetic energy:
Initial Kinetic Energy = (1/2) * 0.650 kg * (20.0 m/s)^2
Next, we can determine the potential energy at the maximum height. The potential energy can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
Given that the mass of the projectile is 0.650 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the maximum height is 12.4 m, we can calculate the potential energy:
Potential Energy = 0.650 kg * 9.8 m/s^2 * 12.4 m
Since energy is conserved, the initial kinetic energy should equal the potential energy at the maximum height. Therefore, we can set the values equal to each other:
(1/2) * 0.650 kg * (20.0 m/s)^2 = 0.650 kg * 9.8 m/s^2 * 12.4 m
Now, we can solve for the unknown, which is the magnitude of the average force due to air resistance. However, in this case, we do not have enough information to determine the magnitude of the average force due to air resistance accurately. Air resistance depends on various factors such as shape, orientation, and speed of the projectile. Without these specific details or an experimental value for the air resistance force, we cannot determine its magnitude.