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A block of mass 5 kg is moving in x-direction with a constant speed 20 m/s. Now it is subjected to a retarding force Fr = – 0.2 x J/m during its travel from x = 10 m to x = 20 m. Its final velocity will be nearly
- a)19.7 m/s
- b)16.4 m/s
- c)14.3 m/s
- d)10 m/s
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A block of mass 5 kg is moving in x-direction with a constant speed 2...
Given data:
- Mass of the block, m = 5 kg
- Initial velocity, u = 20 m/s
- Retarding force, Fr = -0.2x J/m
- Initial position, x1 = 10 m
- Final position, x2 = 20 m
Approach:
To find the final velocity of the block, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
Calculation:
Step 1: Calculate the work done by the retarding force:
The work done by a force is given by the equation:
W = ∫ F dx
where W is the work done, F is the force, and dx is the displacement.
In this case, the retarding force is given by Fr = -0.2x J/m. Substituting the values of x1 and x2, we can calculate the work done as:
W = ∫ Fr dx
= ∫ (-0.2x) dx
= -0.2 ∫ x dx
= -0.2 * [x^2/2]
= -0.1x^2
Now, substituting the values of x1 and x2, we get:
W = -0.1 * [(x2)^2 - (x1)^2]
= -0.1 * [(20)^2 - (10)^2]
= -0.1 * [400 - 100]
= -0.1 * 300
= -30 J
Step 2: Apply the work-energy principle:
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be expressed as:
W = ΔKE
Since the initial kinetic energy, KE1 = 0.5 * m * u^2, and the final kinetic energy, KE2 = 0.5 * m * v^2, we can write:
W = KE2 - KE1
Substituting the values, we have:
-30 = 0.5 * 5 * v^2 - 0.5 * 5 * (20)^2
-30 = 0.5 * 5 * v^2 - 0.5 * 5 * 400
-30 = 0.5 * 5 * v^2 - 0.5 * 2000
-30 = 2.5v^2 - 1000
-30 + 1000 = 2.5v^2
970 = 2.5v^2
v^2 = 970/2.5
v^2 = 388
v ≈ √388
v ≈ 19.7 m/s
Conclusion:
The final velocity of the block is approximately 19.7 m/s. Therefore, the correct answer is option 'A'.
- Mass of the block, m = 5 kg
- Initial velocity, u = 20 m/s
- Retarding force, Fr = -0.2x J/m
- Initial position, x1 = 10 m
- Final position, x2 = 20 m
Approach:
To find the final velocity of the block, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
Calculation:
Step 1: Calculate the work done by the retarding force:
The work done by a force is given by the equation:
W = ∫ F dx
where W is the work done, F is the force, and dx is the displacement.
In this case, the retarding force is given by Fr = -0.2x J/m. Substituting the values of x1 and x2, we can calculate the work done as:
W = ∫ Fr dx
= ∫ (-0.2x) dx
= -0.2 ∫ x dx
= -0.2 * [x^2/2]
= -0.1x^2
Now, substituting the values of x1 and x2, we get:
W = -0.1 * [(x2)^2 - (x1)^2]
= -0.1 * [(20)^2 - (10)^2]
= -0.1 * [400 - 100]
= -0.1 * 300
= -30 J
Step 2: Apply the work-energy principle:
According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be expressed as:
W = ΔKE
Since the initial kinetic energy, KE1 = 0.5 * m * u^2, and the final kinetic energy, KE2 = 0.5 * m * v^2, we can write:
W = KE2 - KE1
Substituting the values, we have:
-30 = 0.5 * 5 * v^2 - 0.5 * 5 * (20)^2
-30 = 0.5 * 5 * v^2 - 0.5 * 5 * 400
-30 = 0.5 * 5 * v^2 - 0.5 * 2000
-30 = 2.5v^2 - 1000
-30 + 1000 = 2.5v^2
970 = 2.5v^2
v^2 = 970/2.5
v^2 = 388
v ≈ √388
v ≈ 19.7 m/s
Conclusion:
The final velocity of the block is approximately 19.7 m/s. Therefore, the correct answer is option 'A'.
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A block of mass 5 kg is moving in x-direction with a constant speed 2...
DW = Fdx
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A block of mass 5 kg is moving in x-direction with a constant speed 20 m/s. Now it is subjected to a retarding force Fr = – 0.2 x J/m during its travel from x = 10 m to x = 20 m. Its final velocity will be nearlya)19.7 m/sb)16.4 m/sc)14.3 m/sd)10 m/sCorrect answer is option 'A'. Can you explain this answer?
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