A sphere rolls on a flat surface with a speed v. What is the kinetic energy of the sphere?
Practice Questions
1 question
Q1
A sphere rolls on a flat surface with a speed v. What is the kinetic energy of the sphere?
(1/2)mv^2
(1/2)mv^2 + (1/5)mv^2
(1/2)mv^2 + (2/5)mv^2
(1/2)mv^2 + (3/5)mv^2
The total kinetic energy of a rolling sphere is the sum of translational and rotational kinetic energy, which is (1/2)mv^2 + (2/5)mv^2.
Questions & Step-by-step Solutions
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Q
Q: A sphere rolls on a flat surface with a speed v. What is the kinetic energy of the sphere?
Solution: The total kinetic energy of a rolling sphere is the sum of translational and rotational kinetic energy, which is (1/2)mv^2 + (2/5)mv^2.
Steps: 5
Step 1: Understand that a sphere rolling on a flat surface has two types of motion: it moves forward (translational motion) and it spins (rotational motion).
Step 2: The formula for translational kinetic energy (the energy due to forward motion) is (1/2)mv^2, where m is the mass of the sphere and v is its speed.
Step 3: The formula for rotational kinetic energy (the energy due to spinning) for a solid sphere is (2/5)mv^2.
Step 4: To find the total kinetic energy of the rolling sphere, add the translational kinetic energy and the rotational kinetic energy together.
Step 5: The total kinetic energy is (1/2)mv^2 + (2/5)mv^2.
