A projectile mass of 0.500 kg is shot straight up with an initial speed of 28.0 m/s.
A. How high would it go if there were no air friction?
I got this answer, it is 40 m.
B. If the projectile rises to a maximum height of only 34.0 m, determine the magnitude of the average force due to air resistance.
The correct answer is 0.865 N but I cannot figure out how to do it. Thanks!
B. The total energy is reduced by
deltaE = 6.0m*g*0.500kg = 29.4 joules at the top of the trajectory
The missing energy goes to doing work against friction, equal to F*34 m = 29.4 J
Therefore F = 29.4J/34m = 0.865 N
(assuming F is constant). If not constant, F is the average force
Okay thank you!!
To determine the magnitude of the average force due to air resistance, we can use the equation for the work done by a force. The work done by a force is equal to the force multiplied by the distance over which the force is applied.
In this case, the force due to air resistance does negative work on the projectile because it acts in the opposite direction to the displacement of the projectile.
The work done by the force due to air resistance can be calculated using the formula:
Work = Force × Distance
Since the projectile rises to a maximum height of 34.0 m, the distance over which the force is applied is 34.0 m.
To find the force, we need to use the formula for work done by a force, which states that:
Work = Change in Kinetic Energy
The change in kinetic energy can be calculated using the formula:
Change in Kinetic Energy = (1/2) × m × (vf^2 - vi^2)
Where m is the mass of the projectile, vf is the final velocity (which is 0 m/s at the maximum height because the projectile momentarily stops), and vi is the initial velocity.
In this case, the mass of the projectile is 0.500 kg, the initial velocity is 28.0 m/s, and the final velocity is 0 m/s.
So, the change in kinetic energy is given by:
Change in Kinetic Energy = (1/2) × 0.500 kg × (0^2 - 28.0^2)
Simplifying this expression, we get:
Change in Kinetic Energy = (1/2) × 0.500 kg × (-28.0^2)
Now, we can equate the work done by the force due to air resistance to the change in kinetic energy:
Force × Distance = Change in Kinetic Energy
Substituting the given values, we have:
Force × 34.0 m = (1/2) × 0.500 kg × (-28.0^2)
Now, we can solve for the force due to air resistance:
Force = [(1/2) × 0.500 kg × (-28.0^2)] / 34.0 m
Evaluating this expression, we find:
Force = 0.865 N
So, the magnitude of the average force due to air resistance is 0.865 N.