Chapter 4: Q82. (page 106)

A ‘doomsday’ asteroid with a mass of $1.0 \times 10^{10} kg$ is hurling through space. Unless the asteroid’s speed is changed by about $0.20 cm / s$ , it will collide with the earth and cause tremendous damage. Researchers suggest that a small ‘space tug’ sent to the asteroid’s surface could exert a gentle, constant force of 2.5 N. For how long must this force act?

Expert verified

This force must be exerted on the asteroid for $8.0 \times 10^{6} s$ .

Step by step solution

The momentum of an object can be identified by evaluating the value of the object’s velocity and mass.The relation is:

$p = m Δ v .$

Here, $m$ is the mass of the object, and $Δ v$ is the change in the velocity.

Given data:

The mass of the asteroid is $m = 1.0 \times 10^{10} kg$ .

The variation in the speed of the asteroid is $Δ v = 0.20 cm / s$ .

The constant force is $F = 2.5 N$ .

The expression for the momentum is given as

$Δ p = m Δ v$ ……. (i)

Also, the momentum is given as

$Δ p = F Δ t$ …… (ii)

Now, equating equations (i) and (ii),

$\begin{matrix} m Δ v = F Δ t \\ Δ t = \frac{m Δ v}{F} \end{matrix}$

Substituting the values in the above expression,

$\begin{matrix} Δ t = \frac{(1.0 \times 10^{10} kg) (0.20 cm / s) (\frac{10^{- 2} m}{1 cm})}{(2.5 N)} \\ Δ t = 8.0 \times 10^{6} s \end{matrix}$

Thus, the time required to exert a constant force is $8.0 \times 10^{6} s$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.