a man pushes a box of mass 5 kg in a horizontal direction by 10 N force on the surface through a distance of 5m if the cofficien of kinetic friction is 0.2 the total work done on the box is
F=F(fr)=μmg
W=F(fr)•s= μmgs
Since
F=F(fr)=μmg,
the work is
W=F(fr)•s= μmgs
To find the total work done on the box, we need to consider both the work done by the applied force and the work done against friction.
First, let's calculate the work done by the applied force. The work done by a force is given by the formula:
Work = Force x Distance x cos(θ)
In this case, the force applied by the man is 10 N, and the distance over which the force is applied is 5 m. The angle (θ) between the applied force and the displacement is 0 degrees since the force is in the same direction as the displacement. Therefore, cos(0) = 1.
So, the work done by the applied force is:
Work_applied = 10 N x 5 m x 1 = 50 N·m or Joules (J)
Now let's consider the work done against friction. The work done against friction is given by the formula:
Work_friction = Force_friction x Distance
The frictional force can be found using the equation:
Force_friction = μ * Normal force
where μ is the coefficient of kinetic friction and Normal force is the force perpendicular to the surface. In this case, since the box is pushed horizontally, the Normal force is equal to the weight of the box, which can be calculated as:
Weight = mass x gravity
Since the mass of the box is 5 kg and the acceleration due to gravity is approximately 9.8 m/s²:
Weight = 5 kg x 9.8 m/s² = 49 N
Now, we can calculate the frictional force:
Force_friction = 0.2 * 49 N = 9.8 N
Finally, we can calculate the work done against friction:
Work_friction = 9.8 N x 5 m = 49 N·m or J
To find the total work done on the box, we need to add the work done by the applied force and the work done against friction:
Total work = Work_applied + Work_friction
Total work = 50 N·m + 49 N·m = 99 N·m or J
Therefore, the total work done on the box is 99 Joules.