Class 11 Exam > Class 11 Questions > Q. A 2 kg block is dropped from a height of 0...
Start Learning for Free
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is?
Verified Answer
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force ...
Mass of the body is ( m ) = 2 Kg
spring's constant ( K ) = 1960 N/m
height of the body = 0.4 m
Let the maximum distance spring will compressed = x m
see the attachment , it is clear that
initial potential energy of body = mg(h + x)
final potential energy = spring potential energy = 1/2 Kx^2
according to law of conservation of energy,
initial potential energy = final potential energy
mg(h + x) = 1/2 Kx^2
2mgh + 2mgx = Kx^2
Kx^2 - 2mgx - 2mgh = 0
⇒ 1960x^2 - 2*2*9.8*x - 2*2*9.8*0.4 = 0
⇒ 1960x^2 - 39.2x - 15.68 = 0
after solving this quadratic equations , we get x = 0.1m
hence, answer is x = 0.1m
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force ...
Problem: A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960 N/m. The maximum compression of the spring is?
Solution:
Given data:
- Mass of the block (m) = 2 kg
- Height (h) = 0.4 m
- Force constant (k) = 1960 N/m
Step 1: Calculate the potential energy of the block
The potential energy (PE) of the block is given by the formula:
PE = mgh
where m is the mass, g is the acceleration due to gravity, and h is the height.
Given: m = 2 kg, g = 9.8 m/s², h = 0.4 m
PE = (2 kg) x (9.8 m/s²) x (0.4 m)
= 7.84 J
Step 2: Calculate the maximum potential energy converted to spring potential energy
The maximum potential energy converted to spring potential energy is given by the formula:
PE_spring = (1/2) k x (x²)
where k is the force constant of the spring and x is the maximum compression of the spring.
Given: k = 1960 N/m
We need to find x.
Step 3: Equating the potential energy of the block to the spring potential energy
Since the potential energy of the block is converted to spring potential energy, we can equate the two equations:
PE = PE_spring
7.84 J = (1/2) (1960 N/m) (x²)
Simplifying:
7.84 J = 980 N/m (x²)
Dividing both sides by 980 N/m:
0.008 = x²
Taking the square root of both sides:
x = √(0.008) m
= 0.089 m
Therefore, the maximum compression of the spring is 0.089 m.
Solution:
Given data:
- Mass of the block (m) = 2 kg
- Height (h) = 0.4 m
- Force constant (k) = 1960 N/m
Step 1: Calculate the potential energy of the block
The potential energy (PE) of the block is given by the formula:
PE = mgh
where m is the mass, g is the acceleration due to gravity, and h is the height.
Given: m = 2 kg, g = 9.8 m/s², h = 0.4 m
PE = (2 kg) x (9.8 m/s²) x (0.4 m)
= 7.84 J
Step 2: Calculate the maximum potential energy converted to spring potential energy
The maximum potential energy converted to spring potential energy is given by the formula:
PE_spring = (1/2) k x (x²)
where k is the force constant of the spring and x is the maximum compression of the spring.
Given: k = 1960 N/m
We need to find x.
Step 3: Equating the potential energy of the block to the spring potential energy
Since the potential energy of the block is converted to spring potential energy, we can equate the two equations:
PE = PE_spring
7.84 J = (1/2) (1960 N/m) (x²)
Simplifying:
7.84 J = 980 N/m (x²)
Dividing both sides by 980 N/m:
0.008 = x²
Taking the square root of both sides:
x = √(0.008) m
= 0.089 m
Therefore, the maximum compression of the spring is 0.089 m.
Community Answer
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force ...
9.1 cm
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
|
Explore Courses for Class 11 exam
|
|
Top Courses for Class 11View all
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is?
Question Description
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is?.
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is?.
Solutions for Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? defined & explained in the simplest way possible. Besides giving the explanation of
Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is?, a detailed solution for Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? has been provided alongside types of Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? theory, EduRev gives you an
ample number of questions to practice Q. A 2 kg block is dropped from a height of 0.4m on a spring of force constant k=1960nm^-1.the maximum compression of the spring is? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup