A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be
- Zero
1.5 ms–1
2.0 ms–1
2.5 ms–1
The Correct Option is C
Solution and Explanation
Given: \(k=12 Nm^{-1}\)
\(F = –kx\)
\(F = –12x\)
\(mv \text{} \frac{dv}{dx} =−12\)
\(\int_{4}^{v}vdx=-6\int_{0.5}^{1.5}xdx\)
(m = 2 kg)
\(\frac{v^2-16}{2}\)=−6[\(\frac{1.5^2-0.5^2}{2}\)]
\(\frac{v^2 -16}{2}\)=−6
v = 2 m/sec
\(\therefore ,\) The correct option is (C): \(2.0\text{ ms}^{-1}\)
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Concepts Used:
Types of Friction
There exists a force called friction which works against the motion between two surfaces that are in contact. Multiple types of friction have been identified, such as static friction, kinetic friction, rolling friction, and fluid friction.
Static friction is the force that opposes the initiation of motion between two surfaces in contact that are not moving relative to each other. It is generally greater than the force of kinetic friction, which is the force that opposes the motion of two surfaces that are in contact and are moving relative to each other. The force of kinetic friction is proportional to the normal force, which is the force perpendicular to the contact surface.
Rolling friction occurs when an object rolls over a surface, such as a wheel rolling on a road. The force of rolling friction is generally less than the force of kinetic friction, which makes it more efficient for transportation.
When an object moves through a fluid like water or air, it experiences fluid friction. The force of fluid friction depends on the object's speed, size, and shape, as well as the properties of the fluid, such as its viscosity.
Also Read: Friction Force Formula
Friction is a fundamental force that affects many aspects of our lives, including transportation, construction, and manufacturing. Understanding the types of friction and their properties is essential for designing and optimizing machines and structures that rely on frictional forces for their function.