Question:
The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is $16.0 \mathrm{~N}$ when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest.
Solution:
Net force is
$\mathrm{T}-2 \mathrm{mg}+2 \mathrm{ma}=0 \ldots \ldots 1$
$\mathrm{T}-\mathrm{mg}-\mathrm{ma}=0 \ldots \ldots 2$
from equation 1 and 2
$a=\frac{T}{4 m}=\frac{16}{4 m}$
$a=\bar{m} \mathrm{~m} / \mathrm{s}^{2}$
Now
$s=u t+\frac{1}{2} a t^{2}$
$s=0+\frac{1}{2} \times \frac{4}{m} \times 1^{2}$
$\mathrm{s}=\frac{2}{m}$
Decrease in P.E. = mgh
P.E. $=(2 \mathrm{~m}-\mathrm{m}) \times 9.8 \times(2 / \mathrm{m})$
P.E. $=19.6 \mathrm{~J}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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