Physics 9-Ch4 (Turning Effect of Forces)-Numerical Problems

 

Table of Contents

• A force of 20 N moves a body with an acceleration
• The weight of a body is 147 N. What is its mass?
• How much force is needed to prevent a body of mass
• Find the acceleration produced by a force of 100 N in a mass of 50 kg
• Does a body weight 20 N. How much force is required to move it vertically upward with an acceleration
• wo masses 52 kg and 48 kg are attached to the ends of a string that passes over a frictionless pulley
• Two masses 26 kg and 24 kg are attached to the ends of a string which passes over a frictionless pulley.
• How much time is required to change 22 Ns momentum by a force of 20 N? (1.1s)
• How much is the force of friction between a wooden block of mass 5 kg and the horizontal marble floor
• How much centripetal force is needed to make a body of mass

A force of 20 N moves a body with an acceleration of 2 $�{�}^{-2}$. What is its mass? (10kg)

Solution:  

Force = F = 20 N
                     Acceleration = a = $2�{�}^{-2}$
                                 Mass = m = ?
                     F = ma

 Or               $�=\frac{�}{�}$
                   $�=\frac{20}{2}$  = 10 kg

The weight of a body is 147 N. What is its mass? (Take the value of g as 10 $�{�}^{-2})$ (14.7 kg)

Solution:     

Weight = w = 147 N
                     Acceleration due to gravity = g = 10 $�{�}^{-2}$  
                     Mass = m = ?
                            w = mg

or                         m =  $\frac{�}{�}$ 
                            m =  $\frac{147}{10}$  
                            m = 14. 7 kg

How much force is needed to prevent a body of mass 10 kg from falling? (100 N)

Solution:     

Mass = m = 50 kg

                    Acceleration = a = g = 10 $�{�}^{-2}$  
                    Force = F = ?
                    F = m a
                    F = $10\times 10$ 
                    F = 100 N

Find the acceleration produced by a force of 100 N in a mass of 50 kg. (

$2�{�}^{-2}$)

Solution:    

Force = F = 100 N
                Mass = m = 50 kg
                Acceleration = a = ?
                F = m a

Or             a =  $\frac{�}{�}$
                a =  $\frac{100}{50}$ 
                a = 2 $�{�}^{-2}$  

Does a body weight 20 N. How much force is required to move it vertically upward with an acceleration of 2 $�{�}^{-2}$? (24 N)

Solution:         

Weight = w = 20 N
                        Acceleration = a = 2 $�{�}^{-2}$
                        Vertically upward force (Tension) = T = ?
                        Fnet  = T – w 
Or                     ma = T – mg
Or                     ma + mg = T
Or                     T = m (a + g) ……………………(i)
Now,                  m = $\frac{�}{�}$ 
                          m =$\frac{20}{10}$= 2 kg

Putting the value of m in Eq.(i), we get
                         T = 2 (2 + 10)
                            = 2(12)
                         T = 24 N

Two masses 52 kg and 48 kg are attached to the ends of a string that passes over a frictionless pulley. Find the tension in the string and acceleration in the bodies when both the masses are moving vertically. $(500�,0.4�{�}^{-2})$

Solution:          

m1 = 52 kg       and       m2 = 48 kg

Tension                T =?   

Acceleration a =?    

  

T =$\frac{(2{�}_1{�}_2)}{({�}_1+{�}_2)}$g

             T = $\frac{(2\times 52\times 48)}{(52+48)}\times$ 10

            T =  $\frac{49920}{100}$ 

            T = 499.20 ≈ 500 N

a =$\frac{({�}_1\text{ –}{�}_2)}{({�}_1+{�}_2)}�$

 

                 a = $\frac{(52-48)}{(52+48)}\times 10$

               a =$\frac{4}{100}\times 10$

                 a  = 0.4 $�{�}^{-2}$ 

Two masses 26 kg and 24 kg are attached to the ends of a string which passes over a frictionless pulley. 26 kg is lying over a smooth horizontal table. 24 N mass is moving vertically downward. Find the tension in the string and the acceleration in the bodies.  (125 N, 4.8 

$�{�}^{-2}$)

Solution:

    m1 = 24 kg       and       m2 = 26 kg

    Tension    T =?   

Acceleration a =?    

  

T =$\frac{({�}_1{�}_2)}{({�}_1+{�}_2)}�$

             T = $\frac{(24\times 26)}{(24+26)}\times$ 10

            T = $\frac{6240}{50}$ 

            T = 124.8 ≈ 125 N

 

a =$\frac{({�}_1)}{({�}_1+{�}_2)}$ g

 

               a = $\frac{24}{(24+26)}\times 10$

               a = $\frac{24}{50}\times 10$

               a  = 4.8 $�{�}^{-2}$ 

How much time is required to change 22 Ns momentum by a force of 20 N? (1.1s)

Solution:      

Change in momentum = Pf – PI = 22 Ns
Force = F = 20 N
Time = t = ?
F =$\frac{({�}_{�}\text{ –}{�}_{�})}{�}$  
t =$\frac{({�}_{�}\text{ –}{�}_{�})}{�}$ 
t =$\frac{22}{20}$= 1.1 S

How much is the force of friction between a wooden block of mass 5 kg and the horizontal marble floor? The coefficient of friction between wood and marble is 0.6. (30 N)

Solution:        

Mass = m = 5 kg
                       Coefficient of friction = µ = 0.6
                        Force of friction = FS = ?
                        FS = µ R                      (where R = mg)
                        FS = µ mg                    
                        FS = $0.6\times 5\times 10$ = 30 N

How much centripetal force is needed to make a body of mass 0.5 kg move in a circle of radius of 50 cm with a speed of 3 

$�{�}^{-1}$? (9 N)   

Solution:         

Mass = m = 0.5 kg
                        Radius of the circle = r = 50 cm =$\frac{50}{100}$= 0.5 m
                        Speed = v = 3 $�{�}^{-1}$
                        Centripetal force = Fc = ?
                                   Fc =$\frac{(��{)}^2}{�}$ 
                                  Fc =$\frac{(0.5\times 3{)}^2}{0.5}$ 
                                 Fc = $\frac{(0.5\times 9)}{0.5}$=$\frac{4.5}{0.5}$= 9 N