Answer :
To find the magnitude of the force of air resistance on the penny, we need to follow these steps:
1. Determine the acceleration of the penny:
- Assume that initially, the penny is at rest, so its initial velocity is 0 m/s.
- The final velocity of the penny after 1.00 second is given as 10.1 m/s.
- Acceleration ([tex]\(a\)[/tex]) is calculated using the formula for uniform acceleration:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}} = \frac{10.1 \, \text{m/s} - 0}{1.0 \, \text{s}} = 10.1 \, \text{m/s}^2
\][/tex]
2. Determine the gravitational force acting on the penny (without air resistance):
- Use the standard acceleration due to gravity ([tex]\(g = 9.81 \, \text{m/s}^2\)[/tex]).
- Assume the mass of the penny is approximately 2.5 grams, which is 0.0025 kg.
- The gravitational force ([tex]\(F_{\text{gravity}}\)[/tex]) is calculated as:
[tex]\[
F_{\text{gravity}} = \text{mass} \times g = 0.0025 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 0.024525 \, \text{N}
\][/tex]
3. Calculate the net force acting on the penny with air resistance:
- The net force ([tex]\(F_{\text{net}}\)[/tex]) is given by the mass of the penny times its acceleration:
[tex]\[
F_{\text{net}} = \text{mass} \times a = 0.0025 \, \text{kg} \times 10.1 \, \text{m/s}^2 = 0.02525 \, \text{N}
\][/tex]
4. Determine the magnitude of the air resistance force:
- The force of air resistance ([tex]\(F_{\text{air resistance}}\)[/tex]) is the difference between the force of gravity and the net force:
[tex]\[
F_{\text{air resistance}} = F_{\text{gravity}} - F_{\text{net}} = 0.024525 \, \text{N} - 0.02525 \, \text{N} = -0.000725 \, \text{N}
\][/tex]
- The negative sign indicates that the air resistance force acts in the opposite direction to gravity.
Thus, the magnitude of the force of air resistance on the penny is approximately [tex]\(0.000725 \, \text{N}\)[/tex].
1. Determine the acceleration of the penny:
- Assume that initially, the penny is at rest, so its initial velocity is 0 m/s.
- The final velocity of the penny after 1.00 second is given as 10.1 m/s.
- Acceleration ([tex]\(a\)[/tex]) is calculated using the formula for uniform acceleration:
[tex]\[
a = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}} = \frac{10.1 \, \text{m/s} - 0}{1.0 \, \text{s}} = 10.1 \, \text{m/s}^2
\][/tex]
2. Determine the gravitational force acting on the penny (without air resistance):
- Use the standard acceleration due to gravity ([tex]\(g = 9.81 \, \text{m/s}^2\)[/tex]).
- Assume the mass of the penny is approximately 2.5 grams, which is 0.0025 kg.
- The gravitational force ([tex]\(F_{\text{gravity}}\)[/tex]) is calculated as:
[tex]\[
F_{\text{gravity}} = \text{mass} \times g = 0.0025 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 0.024525 \, \text{N}
\][/tex]
3. Calculate the net force acting on the penny with air resistance:
- The net force ([tex]\(F_{\text{net}}\)[/tex]) is given by the mass of the penny times its acceleration:
[tex]\[
F_{\text{net}} = \text{mass} \times a = 0.0025 \, \text{kg} \times 10.1 \, \text{m/s}^2 = 0.02525 \, \text{N}
\][/tex]
4. Determine the magnitude of the air resistance force:
- The force of air resistance ([tex]\(F_{\text{air resistance}}\)[/tex]) is the difference between the force of gravity and the net force:
[tex]\[
F_{\text{air resistance}} = F_{\text{gravity}} - F_{\text{net}} = 0.024525 \, \text{N} - 0.02525 \, \text{N} = -0.000725 \, \text{N}
\][/tex]
- The negative sign indicates that the air resistance force acts in the opposite direction to gravity.
Thus, the magnitude of the force of air resistance on the penny is approximately [tex]\(0.000725 \, \text{N}\)[/tex].
