A 149-{\rm g} baseball is dropped from a tree 12.0 m above the ground. If it actually hits the ground with a speed of 7.50 m/s, what is the magnitude of the average force of air resistance exerted on it?
(Average force)*H = Energy lost as work done against air friction
= M g H - (1/2)MV^2
H = 12 m M = 0.149 kg
I don't know what your -{\rm symbiol is supposed to mean, but I know roughly what a baseball's mass is.
Solve for Avg. Force
To determine the magnitude of the average force of air resistance exerted on the baseball, we can use the principle of conservation of energy.
First, we need to calculate the potential energy of the baseball when it is dropped from the tree. The potential energy (PE) is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Mass of baseball (m) = 149 g = 0.149 kg
Height (h) = 12.0 m
Acceleration due to gravity (g) = 9.8 m/s^2
Calculating the potential energy:
PE = (0.149 kg) x (9.8 m/s^2) x (12.0 m)
PE = 17.2176 J
Next, we can calculate the kinetic energy of the baseball just before it hits the ground. The kinetic energy (KE) is given by the equation KE = (1/2)mv^2, where m is the mass and v is the velocity.
Given:
Mass of baseball (m) = 0.149 kg
Velocity just before hitting the ground (v) = 7.50 m/s
Calculating the kinetic energy:
KE = (1/2) x (0.149 kg) x (7.50 m/s)^2
KE = 4.1775 J
According to the principle of conservation of energy, the total energy (E) of the system remains constant. Therefore, the potential energy at the initial height is equal to the kinetic energy just before hitting the ground. So, we have:
E = PE + KE
Plugging in the values:
17.2176 J = 4.1775 J + KE
Solving for KE:
KE = 17.2176 J - 4.1775 J
KE = 13.0401 J
Now, we can calculate the work done by air resistance. The work done (W) is given by the equation W = Fd, where F is the force and d is the distance.
Since the baseball is dropped vertically without any horizontal displacement, the work done by air resistance is equal to the change in mechanical energy:
W = ΔE
W = KE - PE
W = 13.0401 J - 17.2176 J
W = -4.1775 J
The negative sign indicates that the work done by air resistance is against the motion of the baseball.
Finally, we can calculate the magnitude of the average force of air resistance (|F|) using the equation:
|F| = |W| / d
Given:
Distance d = 12.0 m (height of the tree)
Calculating the magnitude of the average force of air resistance:
|F| = |-4.1775 J| / (12.0 m)
|F| = 0.3481 J/m
Therefore, the magnitude of the average force of air resistance exerted on the baseball is 0.3481 J/m.