A horizontal force F pulls a mass m across the floor at constant speed a distance d. If the coefficient of friction between box and floor is u, the work done by the force F is.
I know W= FD and Wf = umgd, but I don't understand what the question asking. Thanks
work=Fd
That is what it is asking.
The question is asking for the work done by the force F in moving the mass m across the floor a distance d. In order to calculate this, we need to take into account the frictional force. The work done by the force F can be calculated using the equation:
Work done by F = Force × Distance
However, since the object is not accelerating and is moving at a constant speed, the net force acting on the object must be zero. This means that the force of friction is equal in magnitude and opposite in direction to the applied force F.
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction × normal force
Since the object is being pushed horizontally, the normal force is equal to the weight of the object, which can be calculated using the equation:
Weight = mass × acceleration due to gravity (g)
Now we can substitute the force of friction into the equation for work:
Work done by F = (Force - Force of friction) × Distance
Substituting the equation for the force of friction:
Work done by F = (Force - umgd) × Distance
Therefore, the work done by the force F in moving the mass m across the floor a distance d is equal to (Force - umgd) × Distance.
The question is asking you to find the work done by the force F in pulling the mass m across the floor a distance d.
First, let's break down the problem and understand the forces at play. The horizontal force F is acting on the mass m, pulling it across the floor. However, there is also a force of friction between the box and the floor, which opposes the motion.
The work done by a force is calculated by multiplying the magnitude of the force (F) by the displacement (d) in the direction of the force. In this case, since the box is being pulled horizontally, the displacement in the direction of the force is equal to the distance d.
To determine the work done by the force F, we need to consider the work done against friction as well. The work done against friction can be calculated using the formula Wf = umgd, where u is the coefficient of friction, m is the mass, g is the acceleration due to gravity, and d is the distance.
Since the box is being pulled at a constant speed, the force F must be equal in magnitude and opposite in direction to the force of friction, so we can say that F = ufN, where N is the normal force.
To find N, we need to consider the force balance in the vertical direction. The weight of the object m is balanced by the normal force N, so N = mg.
Now we can substitute F = ufN and N = mg into the equation for work done by the force F:
W = Fd = (ufN)d = (ufmg)d
Therefore, the work done by the force F is W = (ufmg)d.