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a block of mass 2kg is allowed to fall from a height of 40cm onto a vertical spring constant 1960Nm-. find the maximum compression  produced? answer quickly with all the steps please
7 months ago

Arun
23391 Points

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 Kx²
according to law of conservation of energy,
initial potential energy = final potential energy
mg(h + x) = 1/2 Kx²
2mgh + 2mgx = Kx²
Kx²  - 2mgx - 2mgh = 0
⇒ 1960x² - 2*2*9.8*x - 2*2*9.8*0.4 = 0
⇒ 1960x² - 39.2x - 15.68   = 0
after solving this quadratic equations , we get x = 0.1m
hence, answer is x = 0.1m
7 months ago
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### Course Features

• 731 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions