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Chapter 4: Q82. (page 106)

A 鈥榙oomsday鈥� asteroid with a mass of1.0脳1010kgis hurling through space. Unless the asteroid鈥檚 speed is changed by about0.20cm/s, it will collide with the earth and cause tremendous damage. Researchers suggest that a small 鈥榮pace tug鈥� sent to the asteroid鈥檚 surface could exert a gentle, constant force of 2.5 N. For how long must this force act?

Short Answer

Expert verified

This force must be exerted on the asteroid for 8.0脳106s.

Step by step solution

01

Step 1. Meaning of momentum

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

p=m螖v.

Here,mis the mass of the object, and螖vis the change in the velocity.

02

Step 2. Given information

Given data:

The mass of the asteroid is m=1.0脳1010kg.

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

The constant force is F=2.5N.

03

Step 3. Calculate the time required to exert a constant force

The expression for the momentum is given as

螖p=m螖v鈥︹��. (i)

Also, the momentum is given as

螖p=F螖t鈥︹�� (ii)

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

m螖v=F螖t螖t=m螖vF

Substituting the values in the above expression,

螖t=1.0脳1010kg0.20cm/s10-2m1cm2.5N螖t=8.0脳106s

Thus, the time required to exert a constant force is 8.0脳106s.

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