/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 A horizontal force of \(5 N\) is... [FREE SOLUTION] | 91Ó°ÊÓ

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A horizontal force of \(5 N\) is required to maintain a velocity of \(2 \mathrm{~m} / \mathrm{s}\) for a block of \(10 \mathrm{~kg}\) mass sliding over a rough surface. The work done by this force in one minute is (a) \(600 J\) (b) \(60 J\) (c) \(6 J\) (d) \(6000 J\)

Short Answer

Expert verified
The work done by the force is 600 Joules, hence the correct answer is (a) 600 J.

Step by step solution

01

Understanding the problem and given variables

From the problem, it's clear that a block of 10 kg mass is sliding at a constant speed of 2 m/s under a force of 5 N for 1 minute (or 60 seconds).
02

Calculate distance travelled

The distance travelled by the sliding block can be found by multiplying its velocity (2 m/s) with the time (60 seconds), as distance = speed x time. So, the distance = \(2 m/s \times 60 s = 120 m\)
03

Calculate work done

Now, we apply the formula for work done, which is force x distance. In this case, the force is 5 N and the distance is 120 m. So, the work done = \(5 N \times 120 m = 600 Joules\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Force and Motion
Force and motion are fundamental concepts that describe how objects behave when an external influence is applied. In physics, a force is a push or pull acting upon an object which causes it to change its velocity. This is consistent with Sir Isaac Newton's second law of motion, which states that the acceleration of an object is dependent on two variables: the net force acting upon the object and the mass of the object. The relationship is expressed as \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
  • When a force is exerted on an object, it can cause the object to start moving, stop moving, or change direction.
  • A constant force means that an object will move at a uniform velocity if it already has a certain velocity.
In the exercise, the block is moving at a constant velocity, meaning that the force applied (5 N) precisely counters the forces of friction, resulting in zero net force, as the velocity is unchanged.
Friction
Friction is the resistive force that opposes the motion of an object across a surface. Whenever an object is in motion, it encounters some degree of friction depending on the nature of the contact surface.
  • There are different types of friction such as static, kinetic, and rolling friction.
  • Kinetic friction arises when an object slides over a surface.
In the case of the block in the exercise, kinetic friction is at play, which the applied force must overcome to keep the block moving at a constant speed. This resistance opposes the motion of the block and is what makes the force necessary. The work done, calculated as force multiplied by distance, shows how much energy is used to keep the block moving despite this resistance.
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion. It depends on two main factors: the mass of the object and its speed. The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( KE \) stands for kinetic energy, \( m \) is the mass of the object, and \( v \) is the velocity.
  • Kinetic energy increases with either an increase in mass or speed.
  • It is a scalar quantity, which means it has magnitude but no direction.
In our scenario, the block maintains a constant velocity, hence its kinetic energy remains unchanged over time. The exerted force, working against friction, ensures that the kinetic energy stays stable by not allowing any deceleration of the block. Although the friction does not change the energy directly, the force needs to be consistently applied to maintain the kinetic state of the block.

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Most popular questions from this chapter

One sphere collides with another sphere of same mass at rest inelastically. If the value of coefficient of restitution is \(\frac{1}{2}\), the ratio of their speeds after collision shall be (a) \(1: 2\) (b) \(2: 1\) (c) \(1: 3\) (d) \(3: 1\)

A rubber ball is dropped from a height of \(5 m\) on a planet where the acceleration due to gravity is not known. On bouncing, it rises to \(1.8 m\). The ball loses its velocity on bouncing by a factor of \(\quad\) [CBSE PMT 1998] (a) \(16 / 25\) (b) \(2 / 5\) (c) \(3 / 5\) (d) \(9 / 25\)

The ratio of masses of two balls is \(2: 1\) and before collision the ratio of their velocities is \(1: 2\) in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If \(e=(5 / 6)\), the ratio of speed of each ball before and after collision would be (a) \((5 / 6)\) times (b) Equal(c) Not related (d) Double for the first ball and half for the second ball

A rod of mass \(m\) and length \(l\) is lying on a horizontal table. The work done in making it stand on one end will be (a) \(\mathrm{mgl}\) (b) \(\frac{m g l}{2}\) (c) \(\frac{\mathrm{mgl}}{4}\) (d) \(2 m g l\)

A body of mass \(5 \mathrm{~kg}\) is placed at the origin, and can move only on the \(x\)-axis. A force of \(10 \mathrm{~N}\) is acting on it in a direction making an angle of \(60^{\circ}\) with the \(x\)-axis and displaces it along the \(x\) axis by 4 metres. The work done by the force is (a) \(2.5 J\) (b) \(7.25 J\) (c) \(40 J\) (d) \(20 J\)

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