Numerical Problem Solutions | Chapter 3 Dynamics-I | Physics 9th | New Book | Federal Board

Numerical Problem Solutions
1. A boy is holding a book of mass 2kg. How much force is he applying on the book? If he moves it up with acceleration of 3 m/s2, how much should he apply total force on the book?
Given Data:
Mass of book= m= 2kg
Acceleration=a= 3 ms-2
Find out:
Force is applying on book=F1=?
Total force applied on the book=F=?
Formula:
Applied force= weight of Book
F=w=mg
Total force according to Newton’s second law of motion
F2=ma
Total force applied on the book=F=F1+F2
Solution:
F1= w= mg= (2) (9.8)
F1= 19.6N
F2= ma= (2) (3)
F2 = 6N
Total Force acting on the book=F= F1+ F2 =19.6+6
F=25.6N
Result:
Hence the force applied on the book is 19.6N and the total applied force on the book is 25.6 N.
2. A girl of mass 30kg is running with velocity of 4 m/s. Find the momentum.
Given Data:
Mass= m= 30kg
Velocity=v= 4 ms-1
Find out:
Momentum=P=?
Formula:
P=mv
Solution:
P=mv (30) (4)
P=120kgms-1
OR
P= 120Ns
Result:
The momentum of the girl is 120Ns or 120 kgms-1.
3. A 2kg steel ball is moving with speed of 15 m/s. It hits with bulk of sand and comes to rest in 0.2 seconds. Find force applied by sand bulk on the ball.
Given Data:
Mass of steel ball= m= 2kg
Intial velocity=vi=15ms-1
Final velocity=vf=0ms-1
Tie taken=t=0.2s
Find out:
Force=F=?
Formula:
F=ma
Solution:
First of all find out the value of acceleration “a”:
a= (vf-vi)/t
a= (0-15)/0.2
a= (-15)/0.2
a= -75 ms-2
Now Putting the Values in the formula:
F=ma
F= (2) (-75)
F= -150N
Result:
Hence the force applied by sand bulk on the ball is -150N. Negative sign shows that the reaction of bulk sand on the ball.
4. A 100 grams bullet is fired from 5kg gun. Muzzle velocity of bullet is 20m/s. Find recoil velocity of the gun.
Given Data:
Mass of bullet=mB = 100g = 100/1000 kg = 0.1kg
Mass of gun=mG= 5kg
Velocity of bullet=vB= 20ms-1
Find out:
Velocity of Gun=vG=?
Formula:
vG = - (mB VB)/mG
Solution:
vG = - (mB VB)/mG
vG = - ((0.1)(20))/5 = - 2/5
vG = - 0.4 ms-1
Result:
Hence the gun recoils with velocity - 0.4 ms-1. Negative sign indicated that gun recoils in opposite direction w.r.t bullet velocity.
5. A robotic car of 15 kg is moving with 25 m/s. Brakes are applied to stop it. Braked apply constant force of 50N. How long does the car take to stop?
Given Data:
Mass of robotic car= m= 15kg
Velocity= v= 25ms-1
Apllied braked force=F= 50N
Find out:
Time taken=t=?
Formula:
F= ∆P/t
Solution:
F= ∆P/t
F= mv/t
t= mv/F= F= ((15)(25))/50
t= 375/50
t=7.5s
Result:
Hence 7.5s time is taken by the robotic car to applied brake.
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