Suggested languages for you:

Americas

Europe

Q7PE

Expert-verifiedFound in: Page 161

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) If the rocket sled shown in Figure 4.32 starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is 2100 kg, the thrust T is 2.4×10 ^{4} N, and the force of friction opposing the motion is known to be 650 N. **

**(b) Why is the acceleration not one-fourth of what it is with all rockets burning?**

(a) The magnitude of the acceleration is 11.119 m/s^{2}.

(b) The force of friction is the same for both the cases; therefore, the magnitude of the acceleration is not one-fourth with single rocket burning.

**Significant Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. Mathematically,**

**F _{net} = ma ................(i)**

**Here, F _{net} is the net force, m is the mass, and a is the acceleration.**

The net force acts in the horizontal direction with the addition of engine thrust and the opposition from the friction forces. So, write the expression for the net force considering the two forces.

F_{net }= T - f

Here, f is the friction force, and T is the engine thrust.

Substitute (T-f) for F_{net} in equation (i), and we get,

T - f = ma .............(ii)

- The mass of the system is 2100 kg.
- The thrust T is 2.4×10
^{4}N. - and the force of friction opposing the motion is 650 N.

Substitute 2100kg for m, 2.4x10^{4} N for T, and 650N for f in equation (ii), and we get,

$2.4\times {10}^{4}N-650N=2100kg\times a\phantom{\rule{0ex}{0ex}}23350N=2100kg\times a\phantom{\rule{0ex}{0ex}}a=\frac{23350kg.m/{s}^{2}}{2100kg}\phantom{\rule{0ex}{0ex}}a=11.119m/{s}^{2}$

Hence, the magnitude of the acceleration is 11.119 m/s^{2}.

The magnitude of acceleration for single rocket burning is not one-fourth as in the case of all four rockets burning because the magnitude of the force of friction is the same for both cases.

94% of StudySmarter users get better grades.

Sign up for free