a 840 N crate rests on the floor how much work is required to move it at constant speed 5.5m along the floor against a friction force 180 N?
The force required to move the crate at constant speed should just be greater than the frictional force.
F (ext.)= 180 N
Work done = F*s = 180*5.5 = 990 J
To find out how much work is required to move the crate at a constant speed against the friction force, we need to calculate the work done against friction.
Work is defined as the product of the force applied and the distance moved in the direction of the force. Mathematically, work is given by the equation:
Work = Force * Distance * cos(theta)
In this case, the force applied is the friction force, which is 180 N, and the distance moved is 5.5 m.
However, in this problem, the crate is already at rest, so an additional force needs to be applied to overcome the static friction before the crate starts moving at a constant speed. The applied force needed to overcome static friction is equal in magnitude but opposite in direction to the frictional force. So, we can consider the applied force to be 180 N in the opposite direction.
Now let's calculate the work done against friction:
Work = Friction Force * Distance * cos(theta)
Work = 180 N * 5.5 m * cos(180 degrees)
Note: In this equation, the angle theta between the force and the direction of movement is 180 degrees because the force of friction acts in the opposite direction of motion. The cosine of 180 degrees is -1.
Work = 180 N * 5.5 m * (-1)
Work = -990 J
Therefore, the work required to move the crate at a constant speed of 5.5 m along the floor against the friction force is -990 Joules. The negative sign indicates that work is being done against the direction of motion, which makes sense as we are moving the crate against the friction force.