A jet with mass m 8 104 kg jet accelerates down the runway

A jet with mass m = 8 × 10⁴ kg jet accelerates down the runway for takeoff at 2.4 m/s².

1) What is the net horizontal force on the airplane as it accelerates for takeoff? _____ N

2) What is the net vertical force on the airplane as it accelerates for takeoff? _____ N

3) Once off the ground, the plane climbs upward for 20 seconds. During this time, the vertical speed increases from zero to 18 m/s, while the horizontal speed increases from 80 m/s to 95 m/s. What is the net horizontal force on the airplane as it climbs upward? _____ N

4) What is the net vertical force on the airplane as it climbs upward? ____ N

5) After reaching cruising altitude, the plane levels off, keeping the horizontal speed constant, but smoothly reducing the vertical speed to zero, in 17 seconds. What is the net horizontal force on the airplane as it levels off? _____ N

6) What is the net vertical force on the airplane as it levels off? _____ N

Solution

1) Net Horizontal Force : Ma = 8*10^4 *2.4 =1.92 *10^5 N

2) Vertical Force =0

3)Horizpntal Acceleration = 95-80/20 =.75 m/S^2

Horizontal force = 8*10^4 * .75 =6* 10^4

4)During the 20 seconds, the vertical speed increases from zero to 18 m/s
Vertical acceleration = velocity ÷ time = +18 ÷ 20 = .9 m/s^2
Force causing acceleration = 8.0 * 10^4 * .9 = +7.2 * 10^4

To accelerate the airplane at +1.25 m/s^2 vertically, the net upward force must = weight of plane + Force causing acceleration.

Force = 8.0 * 10^4 * 9.8 + +7.2 * 10^4
Force = 8.56 * 10^5 N

5) 0 since horizontal speed is constant.

6)Next, the vertical speed is reduced from 18 m/s to 0 m/s, in 20 seconds.
Acceleration = velocity ÷ time = -18 ÷ 17 = -(18/17) m/s^2
The vertical force that caused the -(18/17) m/s^2 acceleration =
8.0 * 10^4 * -(18/17) = -8.47 * 10^4 N

Net vertical force on the airplane as it levels off =
+8.56 * 10^5 + -.847 * 10^5 = 7.72 * 10^5 N

The weight = 8.0 * 10^4 * 9.8 = 7.84 * 10^5 N  

To have a vertical velocity of 0 m/s the upward vertical force on the plane must equal its weight!!!


So the plane will not level off at 0 m/s upward, unless the plane increases the vertical force to 7.84 *10^4