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A body of mass 50 kg slides over a horizontal distance of 1 m. If coefficient of friction between their surfaces is 0.2, then work done against friction is
- a)98 J
- b)72 J
- c)56 J
- d)34 J
Correct answer is option 'A'. Can you explain this answer?
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To calculate the work done against friction, we can use the formula:
Work = Force x Distance
1. Determine the force of friction:
The force of friction can be calculated using the formula:
Force of Friction = coefficient of friction x Normal Force
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the body is sliding horizontally, the normal force is equal to the weight of the body, which can be calculated as:
Normal Force = mass x gravity
where gravity is the acceleration due to gravity (approximately 9.8 m/s²).
2. Calculate the force of friction:
Using the given coefficient of friction (0.2) and the weight of the body (mass x gravity), we can find the force of friction:
Force of Friction = 0.2 x (mass x gravity)
3. Calculate the work done against friction:
Now that we have the force of friction, we can calculate the work done against friction by multiplying the force of friction by the distance over which it acts:
Work = Force of Friction x Distance
Given that the distance is 1 m, we can substitute the values into the equation:
Work = (0.2 x mass x gravity) x 1
Since the mass is given as 50 kg and gravity is approximately 9.8 m/s², we can substitute these values:
Work = (0.2 x 50 x 9.8) x 1
= 98 J
Therefore, the work done against friction is 98 J (Option A).
Work = Force x Distance
1. Determine the force of friction:
The force of friction can be calculated using the formula:
Force of Friction = coefficient of friction x Normal Force
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the body is sliding horizontally, the normal force is equal to the weight of the body, which can be calculated as:
Normal Force = mass x gravity
where gravity is the acceleration due to gravity (approximately 9.8 m/s²).
2. Calculate the force of friction:
Using the given coefficient of friction (0.2) and the weight of the body (mass x gravity), we can find the force of friction:
Force of Friction = 0.2 x (mass x gravity)
3. Calculate the work done against friction:
Now that we have the force of friction, we can calculate the work done against friction by multiplying the force of friction by the distance over which it acts:
Work = Force of Friction x Distance
Given that the distance is 1 m, we can substitute the values into the equation:
Work = (0.2 x mass x gravity) x 1
Since the mass is given as 50 kg and gravity is approximately 9.8 m/s², we can substitute these values:
Work = (0.2 x 50 x 9.8) x 1
= 98 J
Therefore, the work done against friction is 98 J (Option A).
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A body of mass 50 kg slides over a horizontal distance of 1 m. If coefficient of friction between their surfaces is 0.2, then work done against friction isa)98 Jb)72 Jc)56 Jd)34 JCorrect answer is option 'A'. Can you explain this answer?
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