Question

A 260-kg glider is being pulled by a 1,940-kg jet along a horizontal runway with an acceleration of a= 2.20 m/s^2 to the right. Find the following:
a. the magnitude of the thrust provided by the jet's engines.
b. the magnitude of the tension in the cable connecting the jet and glider

Answer 1

Answer:

a) The magnitude of the thrust provided by the jet's engines is 4840 newtons.

b) The magnitude of the tension in the cable connecting the jet and glider is 572 newtons.

Explanation:

a) By Newton's laws we construct the following equations of equilibrium. Please notice that both the glider and the jet experiments has the same acceleration:

Jet

$\Sigma F = F - T = m_{J}\cdot a$ (1)

Glider

$\Sigma F = T = m_{G}\cdot a$ (2)

Where:

$F$ - Thrust of jet engines, measured in newtons.

$T$ - Tension in the cable connecting the jet and glider, measured in newtons.

$m_{G}$, $m_{J}$ - Masses of the glider and the jet, measured in kilograms.

$a$ - Acceleration of the glider-jet system, measured in meters per square second.

If we know that $m_{G} = 260\,kg$, $m_{J} = 1,940\,kg$ and $a = 2.20\,\frac{m}{s^{2}}$, then the solution of this system of equations:

By (2):

$T = (260\,kg)\cdot \left(2.20\,\frac{m}{s^{2}} \right)$

$T = 572\,N$

By (1):

$F = T+m_{J}\cdot a$

$F = 572\,N+(1,940\,kg)\cdot \left(2.20\,\frac{m}{s^{2}} \right)$

$F = 4840\,N$

The magnitude of the thrust provided by the jet's engines is 4840 newtons.

b) The magnitude of the tension in the cable connecting the jet and glider is 572 newtons.