The acceleration of One of Four rockets Burning| Newton’s Second Law of Motion: Concept of a System| Dynamics| College Physics| Problem 4.7

PROBLEM:

(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 24,000 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?

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SOLUTION:

PART A

If we look at the given figure, there are two forces responsible for the motion of the object in the horizontal direction–the thrust and the friction. We can state that the net force is equal to thrust minus friction. We are also given based from the discussion of the College Physics book that T=25,900 Newtons. Based from Newton’s second law of motion, we can calculate for the acceleration as

net\:F=ma

a=\frac{net\:F}{m}

a=\frac{T-f}{m}

a=\frac{25900\:N-650\:N}{2,100\:kg}

a=12.0238\:m/s^2

PART B

The magnitude of the acceleration depends on two forces–the thrust and the friction. Since the magnitude of the friction is the same no matter how many rockets are burning, then the acceleration can not be 1/4 when only 1 of the four rockets are burning. 

 

 

 

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