a box initially moving with a speed of 5m/s along a rough , horizontal floor , it stopped it after 5 m the conffenict friction is 0.3 find the work done by friction .
To find the work done by friction, we need to use the formula:
Work = Force x Distance
In this case, the force of friction can be calculated using the equation:
Force of friction = coefficient of friction x Normal force
The normal force of an object on a horizontal surface is equal to the weight of the object, which is given by:
Normal force = mass x gravity
Given that the initial speed of the box is 5 m/s and it comes to a stop after traveling a distance of 5 m, we can assume that the box is decelerating uniformly. The final velocity is 0 m/s.
Using the equation of motion, we have:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s)
u = initial velocity (5 m/s)
a = acceleration
s = distance (5 m)
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
= (0^2 - 5^2) / (2 * 5)
= -25 / 10
= -2.5 m/s^2 (The negative sign indicates deceleration)
The force of friction can then be calculated using:
Force of friction = coefficient of friction x Normal force
= 0.3 x (mass x gravity)
To find the mass, we need to use the equation:
Weight = mass x gravity
= force due to gravity
Since the object is on a horizontal surface, there is no vertical motion, so the weight is equal to the normal force:
Normal force = Weight = mass x gravity
Substituting this into the equation for the force of friction:
Force of friction = 0.3 x Normal force
= 0.3 x (mass x gravity)
Now, we can substitute the values into the equation:
Force of friction = 0.3 x (mass x gravity)
= 0.3 x (mass x 9.8 m/s^2)
The work done by friction is given by:
Work = Force x Distance
= (0.3 x (mass x 9.8 m/s^2)) x distance
Substituting the values we have:
Work = (0.3 x (mass x 9.8 m/s^2)) x 5 m
To find the work done by friction, we need to know the mass of the box. Please provide the mass of the box so we can continue with the calculation.