A 19.5 kg block is dragged over a rough, horizontal surface by a constant force of 110 N
acting at an angle of angle 31.1◦ above the horizontal. The block is displaced 6.74 m,and the coefficient of kinetic friction is 0.156.What is the net work done on the block?
Answer in units of J.
This look s like one I answered already, posted by you.
I did it the way you said and it said it was wrong.
The answer is 433.719 joules. You find the sum of the x forces by taking 110*cos31.1 - 19.5*9.81*.156 which gives you 64.35 Newtons. You put that answer in the Work formula. Work equals force * distance so take 64.35*6.74 meters and you get your answer, 433.719 Joules.
Nate, the friction force is equal to mu*N, N is equal to mg-Fsin(31.1) not mg.
But you do not need the frictional force to find the total work. Just the dragging force and the displacement.
To find the net work done on the block, we need to consider the work done by the applied force and the work done by the friction force.
1. Work done by the applied force:
The work done by a force can be calculated using the formula:
Work = Force * Distance * cos(theta),
where Force is the magnitude of the force applied, Distance is the displacement, and theta is the angle between the force and the displacement.
In this case, the magnitude of the applied force is 110 N, the displacement is 6.74 m, and the angle is 31.1 degrees above the horizontal. However, since the force is acting in the same direction as the displacement, the angle we need to use is 180 degrees - 31.1 degrees = 148.9 degrees.
So, the work done by the applied force is:
Work_applied = 110 N * 6.74 m * cos(148.9 degrees).
2. Work done by the friction force:
The friction force acts opposite to the direction of motion and does negative work. The work done by the friction force can be calculated using the formula:
Work_friction = -Friction force * Distance,
where Friction force = coefficient of friction * normal force.
In this case, the coefficient of kinetic friction is 0.156. The normal force is the force exerted by the surface perpendicular to the block's motion, given by:
Normal force = mass * gravity,
where mass = 19.5 kg and gravity = 9.8 m/s^2.
So, the friction force is:
Friction force = 0.156 * (19.5 kg * 9.8 m/s^2).
Now we can calculate the work done by the friction force:
Work_friction = -(0.156 * (19.5 kg * 9.8 m/s^2)) * 6.74 m.
Finally, we can find the net work done on the block by adding the work done by the applied force and the work done by the friction force:
Net work = Work_applied + Work_friction.
Now, plug the values into the equations and calculate to find the net work done on the block in Joules (J).