G. Solve the following numerical problems.
1. Calculate the work done on the body by a force of 500 N if the body moves 7.5 m in
the direction of the force.
2. Find out the magnitude of force acting on a box when 1000 J of work is done to displace it by 5 m.
3. A load of mass 30 kg is lifted up by 7.0 m. Calculate the work done. (Take g = 9.8 m s.)
4. A 20-kg ball is thrown upward with a speed of 4 m s-1.
(a) Find its potential energy when it
reaches the highest point.
(b) Calculate the maximum height it
reaches.
Answers
Answer:
- (1) Work Done = 3750 J
- (2) Force = 200 N
- (3) Work Done = 2058 J
- 4(a) Potential Energy = 158.76 J
- 4(b) Maximum height = 0.81 metres
Explanation:
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(1)
when some force acting on body & produce displacemet in the body. Then , we say that the work is done.
• W = Fs
Substitute the value we get
→ W = 500 × 7.5
→ W = 50×75
→ W = 3750 J
- Hence, the work done is 3750 Joules.
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(2)
Force is defined as the product of mass and acceleration.
As we have to calculate the magnitude force .
• W = Fs
substitute the value we get
→ 1000 = F × 5
→ F = 1000/5
→ F = 200 N
- Hence, the magnitude of force is 200 newton.
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(3)
Here, we have to calculate the work done by body in against gravity .
• W = mgh
substitute the value we get
→ W = 30 × 9.8 × 7
→ W = 3 × 98 × 7
→ W = 21 × 98
→ W = 2058 J
- Hence, the work done by the body is 2058 Joules.
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(4)
(b)
Firstly we calculate the maximum height attained by the ball .
Using 3rd Equation of Motion
• v² = u² +2as
Substitute the value we get
→ 0² = 4² + 2× (-9.8) × s
→ 0 = 16 + (-19.6) × s
→ -16 = -19.6 × s
→ s = -16/-19.6
→ s = 16/19.6
→ s = 0.81 m
(a)
Now, Calculating the Potential Energy .
• PE = mgh
Substitute the value we get
→ PE = 20 × 9.8 × 0.81
→ PE = 98 × 2 × 0.81
→ PE = 158.76 J
- Hence, the potential energy is 158 .76 Joules.
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Answer:
Solution No ❶ .
Given :
- A force of 500 N if the body moves 7.5 m.
To Find :-
- What is the work done on the body.
Formula Used :-
✪ Work done = Force × Displacement ✪
Solution :-
Given :
- Force = 500 N
- Displacement = 7.5 m
According to the question by using the formula we get,
⇒ Work done = 500 × 7.5
➠ Work done = 3750 J
∴ The work done on the body by the force is 3750 J .
_____________________
Solution No ❷ .
Given :
- A box when 1000 J of work is done to displace it by 5 m.
To Find :-
- What is the magnitude of force.
Formula Used :-
★ Force = Work done/Displacement ★
Solution :-
Given :
- Work done = 1000 J
- Displacement = 5 m
According to the question by using the formula we get,
⇒ Force = 1000/5
➠ Force = 200 N
∴ The magnitude of force acting on a box is 200 N .
_________________________
Solution No ❸ .
Given :
- A load of mass 30 kg is lifted up by 7.0 m. (g = 9.8 m/s)
To Find :-
- What is the work done.
Formula Used :-
✪ Work done = mgh ✪
where,
- m = Mass
- g = Acceleration due to gravity
- h = Height
Solution :-
Given :
- Mass = 30 kg
- Acceleration due to gravity = 9.8 m/s
- Height = 7.0 m
According to the question by using the formula we get,
⇒ Work done = 30 × 9.8 × 7.0
⇒ Work done = 294 × 7.0
➠ Work done = 2058 J
∴ The work done is 2058 J .
__________________________
Solution No ❹ .
Given :
- A 20 kg of ball is thrown upward with a speed of 4 m/s.
To Find :-
- What is the potential energy when it reaches the highest point.
- What is the maximum height it reaches.
Formula Used :-
✪ v² = u² + 2as ✪
where,
- v = Final velocity
- u = Initial velocity
- a = Acceleration due to gravity
- s = Distance covered
✯ P.E = mgh ✯
where,
- P.E = Potential Energy
- m = Mass
- g = Acceleration due to gravity
- h = Height
Solution :-
First we have to find the distance covered,
Given :
- Final velocity = 0 m/s
- Initial velocity = 4 m/s
- Acceleration due to gravity = - 9.8 m/s
According to the question by using the formula we get,
⇒ (0)² = (4)² + 2(- 9.8) × s
⇒ 0 = 16 + - 19.6 × s
⇒ - 16 = - 19.6 × s
⇒ - 16/- 19.6 = s
⇒ 0.81 = s
➠ s = 0.81 m
∴ The maximum height is 0.81 m .
Now, we have to find the potential energy,
Given :
- Mass = 20 kg
- Acceleration due to gravity = 9.8 m/s
- Height = 0.81 m
According to the question by using the formula we get,
↦ P.E = 20 × 9.8 × 0.81
↦ P.E = 196 × 0.81
➦ P.E = 158.76 J
∴ The potential energy is 158.76 J .