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.