Question

(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 2.4×10⁴ 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?

Short answer

(a) The magnitude of the acceleration is 11.119m/s².

(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.

Step-by-step solution

Concept of Newton’s second law of motion.

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)

Given Data

• The mass of the system is 2100 kg.
• The thrust T is 2.4×10⁴ N.
• and the force of friction opposing the motion is 650 N.

(a) Determine the magnitude of the acceleration

Substitute 2100kg for m, 2.4x10⁴ N for T, and 650N for f in equation (ii), and we get,

$$\begin{gathered} 2.4\times {10}^{4}N-650N=2100kg\times a \\ 23350N=2100kg\times a \\ a=\frac{23350kg.m/s^2}{2100kg} \\ a=11.119m/s^2 \end{gathered}$$

Hence, the magnitude of the acceleration is 11.119 m/s².

(b) Reason for acceleration not being one-fourth

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.