A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75 m and 2 m respectively, its maximum speed will be
Speed is a scalar quantity that measures how quickly an object moves. It is defined as the distance traveled per unit of time. Speed can be constant or variable, depending on the motion of the object. Common units of speed include meters per second and kilometers per hour. Understanding speed is essential in various fields, including physics, engineering, and everyday life.
Class 11 Physics Chapter 5 focuses on work, energy and power essential concepts in mechanics. It covers definitions calculations and relationships between work, energy and power. Understanding these concepts is crucial for analyzing physical systems and solving problems related to motion and forces in the CBSE exam for 2024-25.
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To find the maximum speed of the child on the swing, we use the principle of conservation of energy. The total mechanical energy is conserved, so the loss in potential energy is converted to kinetic energy at the lowest point.
Step 1: Calculate the change in potential energy
The difference in height between the maximum and minimum positions is:
h = Maximum height − Minimum height
h = 2 m − 0.75 m
h = 1.25 m
Step 2: Apply conservation of energy law
At the highest point all the energy will be potential. At the lowest point, it will be the kinetic energy where the potential is converted into this kinetic energy.
K.E = P.E.
(1/2)mv² = mgh
Given:
– m = mass of child (gets eliminated on both the sides)
g = acceleration due to gravity = 10 m/s²
h = height = 1.25 m
– v = maximum speed
Rearrange the equation to find v:
v² = 2gh
v = √(2gh)
Substitute the values:
nv = √(2 × 10 × 1.25)
nv = √(25)
nv = 5 m/s
The maximum speed of the child on the swing is 5 m/s.
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