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?

Answer 1

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.