Question

A baseball with mass of 0.145 kg is thrown straight down at the ground. At a particular speed, it has a drag force of 0.4 N acting on it. What is its acceleration at that time? :)

Answer 1

To determine the acceleration of the baseball when it is thrown straight down and is experiencing a drag force, we can use Newton's second law of motion, which states that:

\[
F_{net} = m \cdot a
\]

where \( F_{net} \) is the net force acting on the object, \( m \) is the mass of the object, and \( a \) is its acceleration.

The forces acting on the baseball are the gravitational force (weight) and the drag force. The gravitational force can be calculated using:

\[
F_{gravity} = m \cdot g
\]

where \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \).

1. Calculate the gravitational force acting on the baseball:

\[
F_{gravity} = 0.145 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 1.42145 \, \text{N}
\]

2. The drag force is acting upwards and is given as \( 0.4 \, \text{N} \). Therefore, we can express the net force as:

\[
F_{net} = F_{gravity} - F_{drag}
\]

Substituting in the values we found:

\[
F_{net} = 1.42145 \, \text{N} - 0.4 \, \text{N} = 1.02145 \, \text{N}
\]

3. Now use Newton's second law to find the acceleration:

\[
F_{net} = m \cdot a
\]

\[
a = \frac{F_{net}}{m} = \frac{1.02145 \, \text{N}}{0.145 \, \text{kg}} \approx 7.04 \, \text{m/s}^2
\]

Thus, the acceleration of the baseball at that speed is approximately \( 7.04 \, \text{m/s}^2 \) downward.