Answered: Calculate the acceleration of the 2000…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter5: Newton's Law Of Motion

Section: Chapter Questions

Problem 31P: What is the deceleration of the rocket sled if it comes to rest in 1.10 s from a speed of 1000.0...

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Question

Calculate the acceleration of the 2000 kg twin engine aircraft just before takeoff when the thrust of the engines is 1100 n . Assuming a constant acceleration of 1.5 m/s^2 , how long would it take to attain a speed of 28 m/s at which speed it could lift off ? Starting from rest , how far would the plane travel if accelerating at 1.5 m/s^s after 30 seconds ?

Expert Solution

Step 1

From Newton's law the expression for force is

$\begin{array}{rcl} a & = & \frac{F}{m} \\ = & \frac{1100 N}{2000 kg} \\ = & 0.55 \frac{m}{s^{2}} \end{array}$

Therefore, the acceleration just before take off is $\begin{array}{rcl} 0 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 55 \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} \frac{m}{s^{2}} \end{array}$

The expression to find the time to attain certain speed with uniform acceleration is

$t = \frac{v - u}{a'}$

Assuming the air craft started from rest, u=0

$\begin{array}{rcl} t & = & \frac{28 \frac{m}{s} - 0 \frac{m}{s}}{1.5 \frac{m}{s^{2}}} \\ = & 18.6667 s \\ \approx & 19 s \end{array}$

Therefore, the time to attain speed is 19 s.

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