a body at rest starts moving at 36 km/h if 100 N of force acts 2sec . find the mass of the body . if the same body is moving 36km/h and is brought to rest in 2 seconds would the same force have acted? what is the difference between 2 cases
Answers
Answer:
- Magnitudes of forces applied in both cases are same, but directions are just opposite.
Explanation:
In Case (I)
Given that,
- Initial velocity of body, u = 0
- Final velocity of body, v = 36 km/h = 36 * 5/18 m/s = 10 m/s
- time taken for change in velocity, t = 2 sec
- Force applied, F = 100 N
We need to find,
- Mass of body, m =?
Solution,
Let, acceleration of body be a
Using First equation of motion
→ v = u + a t
→ 10 = 0 + a ( 2 )
→ a = 5 m/s²
Using newton's second law
→ F = m a
→ 100 = m · ( 5 )
→ m = 100/5 = 20 kg
Therefore,
- Mass of body is 20 kg.
Now,
In case (II)
Given,
- Initial velocity of the same body, u' = 36 km/h = 36 * 5/18 m/s = 10 m/s
- Final velocity of same body, v' = 0
- Time taken to come to rest, t' = 2 s
To find,
- Force acted on body, F' =?
Solution,
Let, acceleration of body be a'
and taking mass of same body as m = 20 kg
Using first equation of motion
→ v' = u' + a' t'
→ 0 = 10 + A ( 2 )
→ A = -5 m/s²
Using Newton's second law of motion
→ F' = m a'
→ F' = ( 20 ) · ( -5 )
→ F' = -100 N
Hence,
- New force will be equal to -100 N.
Now, Considering the results
we can conclude that
- In both cases the magnitudes of the forces applied on the bodies are same, but the directions are opposite.
- In the first case Force applied is equal to positive 100 Newtons and in second case force applied is equal to negative 100 Newton. that shows that the direction of forces applied are opposite to each other.
Answer :-
• Hence we get, mass of the body = 20 Kg.
• Hence we can say that, in both the cases direction of forces applied are different but magnitude is same to 100 N.
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★ Concept :-
Here the concept of Force and First equation of Motion is used. According to this, when Force is applied on the body, this force depends on its mass and acceleration. This is given as,
• Force(F) = Mass(m) × Acceleration (a)
This is also known as Newton's Second Law of Motion.
Also, here the concept of Newton's First Equation of Motion has been used. According to this,
• v - u = at
where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.
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★ Question :-
A body at rest starts moving at 36 km/h if 100 N of force acts 2sec . Find the mass of the body . If the same body is moving at 36km/h and is brought to rest in 2 seconds would the same force have acted ? What is the difference between 2 cases ?
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★ Solution :-
Let us solve this question line by line and problem by problem. Then,
~ Case I :-
Given,
» Final velocity of the body = v
= 36 Km/h = {36 × (5/18)} m/sec
= 10 m/sec
» Force applied on the body = F = 100 N
»Initial velocity of the body = u = 0 Km/h
= 0 m/sec
(since the body starts from rest)
» Time taken for tthe body = t = 2 sec
→ Let the acceleration of the body be 'a' m/sec²
→ Let the mass of the body be 'm' Kg
Using the Second Equation of Motion, we get,
✒ v - u = a × t
By applying values,
✒ 10 - 0 = a × 2
✒ a × 2 = 10
⇒
✒ a = 5 m/sec²
Here the acceleration is in m/sec² which is the standard form, to be checked using Dimensional Formula. So we can directly apply in our Second Law of Motion.
So,
✒ F = m × a
By applying values, we get,
✒ 100 = m × 5
✒ m = 100/5
✒ m = 20 Kg
Hence we get, mass of the body = 20 Kg.
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~ Case II :-
Given,
» Mass of the body = m = 20 Kg
» Initial Velocity = u = 36 Km/hr = {36 × (5/18)} m/sec
= 10 m/sec
» Final Velocity = v = 0 Km/hr = 0 m/sec
» Time Taken = t = 2 seconds
→ Let the acceleration of the body be 'a'
→ Let the Force acting upon body be 'F'
Similarly, the as Case I, using First Equation of Motion :-
✒ 0 - 10 = a × 2
✒ a × 2 = -10
⇒ 
✒ a = - 5 m/sec²
Here, there is -ve acceleration which shows that retardation happens and body is brought to rest from motion by opposing the force.
Now applying, this value of Acceleration in the Second Law of Motion, we get,
✒ F = m × a
✒ F = 20 Kg × (-5) m/sec²
✒ F = -100 N
Hence the force applied on body = -100 N
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★ Comparison :-
✏ No the force applied on body in first case is not as same as the force applied in body in second case.
This is because of the following reasons :-
- In case I, the force is acting in direction of motion of the body to make it move with certain velocity. But in case II, the force is acting in opposite direction of motion of body. This makes body come at rest from certain velocity.
- Also in case I, there is positive acceleration that is the body is moving along the direction of motion and its velocity increases. But in case II, there is negative acceleration which shows that body moves in opposite side of motion and its velocity decreases.
- Also, in case I, there is positive force which makes us believe that body is moving and force is applied in certain direction with motion. But in case II, there is negative force which shows that body moves and force is applied in opposite direction to the case I.
Hence we can say that, in both the cases direction of forces applied are different but magnitude is same to 100 N.
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★ More to know :-
•Newton's Second Equation of Motion :-
=> s = ut + ½ at²
where, s is the displacement.
• Newton's Third Equation of Motion :-
=> v² - u² = 2as
• Second Law of Motion states that the rate of change of linear momentum of the body is directly proportional to the applied force and the change takes place in the direction of the applied force.
• First Law of Motion states that every body continues in its state of rest or of motion until or unless an external force is applied to change that state.
• Third Law of Motion states that to every action, there is always an equal and opposite reaction.