136,766 views
39 votes
39 votes
A baseball is thrown straight upward. Describe the direction and magnitude of the velocity, force of gravity, and the varying air resistance force as the ball rises. Explain whether the net force increases, decreases, or is unaffected by the air resistance force. Repeat for the part of the motion when the ball is at maximum height and the part of the motion when the ball is moving downward.

User Spencer Cooley
by
2.5k points

1 Answer

28 votes
28 votes

The characteristics of the vertical throw and Newton's second law allows finding the results for the questions about the motion of the ball with air resistance are:

For the upward movement. The speed of the ball decreases with height of the ball. The forces of gravity and friction go in the same direction.

For the point of maximum height, the velocity is zero and the net force is only the force of gravity.

The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.

Kinematics analyzes the movement of bodies looking for relationships between the position, velocity, and acceleration of bodies.

Newton's second law relates the net force to the mass and the acceleration of the body.

In this case, there is a vertical launch where the ball is launched with an initial velocity and is subjected to an acceleration given by the acceleration of gravity with a vertically downward direction, therefore the speed of the ball must decrease with increasing height.

v² = v₀² - 2g y

Where v and v₀ are the current and initial velocities, respectively, g is the acceleration of gravity, and y is the height of the body.

In the attached, we can see a free-body diagram of the ball, the interaction with the earth is constant and is directed towards the center of the earth, in a vertical direction. The friction force of the air is the opposition of the air to the movement of the ball and is directed opposite the direction of movement of the ball. In the case of the ascending ball, the friction force is directed downwards.

Write Newton's second law for upward motion

-W- fr = m a

-m g - fr = ma

Therefore, we see that the two forces go in the same direction, and therefore the net force increases and the acceleration in the opposite direction of the speed also increases.

At the point of maximum height, the speed of the ball is zero, therefore the friction forces of the air are also zero, at this point the acceleration is equal to the acceleration of gravity.

In the case of the ball lower. Speed ​​increases as the ball descend.

Newton's second law is.

-W + fr = ma

- m g + fr = ma

In this case, we see that the forces go in the opposite direction, therefore the net force on the body decreases.

If the friction force with the air increases with the speed, the point where it is equal to the forces of gravity and the acceleration is zero, from this point the ball goes down with constant speed.

In conclusion with the characteristics of the vertical launch and Newton's second law, we can find the results for the questions about the motion of the ball with air resistance are:

The ball is in a downward movement. The speed increases as the height decreases. The friction force and gravity have the opposite direction, therefore the net force decreases until reaching zero, from this point the speed remains constant.

For the upward movement. The speed of the ball decreases with height of the ball. The forces of gravity and friction go in the same direction.

For the point of maximum height, the velocity is zero and the net force is only the force of gravity.

User Tlastowka
by
2.7k points