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Chapter 5: Q19P (page 118)

A $500 kg$ rocket sled can be accelerated at a constant rate from rest to $1600 km / h$ in $1.8 s$ . What is the magnitude of the required net force?

Short Answer

Expert verified

The magnitude of the required force is $1.23 脳 10^{5} N$ .

Step by step solution

01

The given data

Mass of the rocket, $m = 500 kg$ .
Initial velocity of the rocket, $v_{i} = 0 m / s$
Final velocity of the rocket, $v_{f} = 1600 km / hr o r 444.44 m / s$ .
Rate of constant acceleration, $t = 1.8 s$ .

02

Understanding the concept of kinematics

As we are given the change in velocity in the given period, we can find the acceleration of the rocket.

We already have the mass of the rocket, using Newton鈥檚 2nd law we can find the net force acting on it.

Formula:

Force according to Newton鈥檚 second law, $F = m a$ (i)

Acceleration of a body in motion, $a = \frac{鈭� V}{鈭� t}$ (ii)

03

Calculation of magnitude of the force

Using equation (i), we get the magnitude of the force on the rocket as:

$F = 500 kg 脳 \frac{444.44 m / s}{1.8 s} (鈭� from equation (ii), a = \frac{v_{f} - v_{i}}{t}) = 1.23 脳 10^{5} N$

Hence, the value of force is $1.23 脳 10^{5} N$ .

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