Question
The force that stops a jet plane as it lands on the flight deck of an aircraft carrier is provided by a series of arresting cables. These cables act like extremely stiff rubber bands, stretching enough to keep from slowing the plane down too suddenly. A Hornet jet with a mass of 1.3 x 104 kg lands with an acceleration of –27.6 m/s2. How large is the unbalanced force that the arresting cables exert on the plane?
Answers
GPT-4o mini
To find the unbalanced force exerted by the arresting cables on the jet plane, we can use Newton's second law of motion, which states:
\[
F = m \cdot a
\]
where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.
Given:
- The mass of the Hornet jet \( m = 1.3 \times 10^4 \, \text{kg} \)
- The acceleration \( a = -27.6 \, \text{m/s}^2 \) (the negative sign indicates deceleration).
Now we can substitute the values into the formula:
\[
F = (1.3 \times 10^4 \, \text{kg}) \cdot (-27.6 \, \text{m/s}^2)
\]
Calculating this:
\[
F = 1.3 \times 10^4 \cdot -27.6
\]
\[
F = -35868 \, \text{N}
\]
The negative sign indicates that the force is acting in the opposite direction of the plane's motion (it is a decelerating force). The magnitude of the unbalanced force exerted by the arresting cables on the plane is:
\[
35868 \, \text{N}
\]
Thus, the magnitude of the unbalanced force is **35868 N**.
\[
F = m \cdot a
\]
where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.
Given:
- The mass of the Hornet jet \( m = 1.3 \times 10^4 \, \text{kg} \)
- The acceleration \( a = -27.6 \, \text{m/s}^2 \) (the negative sign indicates deceleration).
Now we can substitute the values into the formula:
\[
F = (1.3 \times 10^4 \, \text{kg}) \cdot (-27.6 \, \text{m/s}^2)
\]
Calculating this:
\[
F = 1.3 \times 10^4 \cdot -27.6
\]
\[
F = -35868 \, \text{N}
\]
The negative sign indicates that the force is acting in the opposite direction of the plane's motion (it is a decelerating force). The magnitude of the unbalanced force exerted by the arresting cables on the plane is:
\[
35868 \, \text{N}
\]
Thus, the magnitude of the unbalanced force is **35868 N**.