a girl pulls a wagon along a level path for a distance of 15.0 m. the handle of the wagon makes an angle of 20.0 degrees with the horizontal, the girl exerts a force of 35.0 N on the handle. Friction provides a force of 24.0 N. Find the net work done on the wagon.
a girl pulls a wagon along a level path for a distance of 15.0 m. the handle of the wagon makes an angle of 20.0 degrees with the horizontal, the girl exerts a force of 35.0 N on the handle. Friction provides a force of 24.0 N. Find the net work done on
To find the net work done on the wagon, we need to consider the work done by the girl and the work done by friction. The net work is the sum of these two works.
1. Work done by the girl:
The component of the force applied by the girl in the direction of motion is given by:
Force in the direction of motion = Force * cos(angle)
Force in the direction of motion = 35.0 N * cos(20.0°)
Force in the direction of motion = 35.0 N * 0.9397
Force in the direction of motion = 32.79 N
The work done by the girl is given by:
Work by the girl = Force in the direction of motion * distance
Work by the girl = 32.79 N * 15.0 m
Work by the girl = 491.85 J
2. Work done by friction:
The work done by friction is given by:
Work by friction = Force of friction * distance
Work by friction = 24.0 N * 15.0 m
Work by friction = 360 J
3. Net work done:
The net work done is the sum of the work done by the girl and the work done by friction:
Net work done = Work by the girl + Work by friction
Net work done = 491.85 J + 360 J
Net work done = 851.85 J
Therefore, the net work done on the wagon is 851.85 J.
To find the net work done on the wagon, we need to calculate the work done by the girl and the work done by friction and then subtract the two.
First, let's calculate the work done by the girl. The work done by a force can be calculated using the formula:
Work = Force × Distance × cos(θ)
where θ is the angle between the force and the direction of motion.
In this case, the force exerted by the girl is 35.0 N and the distance is 15.0 m. The angle between the force and the direction of motion is 20.0 degrees.
So, the work done by the girl is:
Work_girl = 35.0 N × 15.0 m × cos(20.0 degrees)
Next, let's calculate the work done by friction. The work done by friction can be calculated using the formula:
Work = Force × Distance
In this case, the force of friction is 24.0 N and the distance is 15.0 m.
So, the work done by friction is:
Work_friction = 24.0 N × 15.0 m
Finally, let's calculate the net work done on the wagon:
Net Work = Work_girl - Work_friction
Substitute the values we calculated earlier:
Net Work = (35.0 N × 15.0 m × cos(20.0 degrees)) - (24.0 N × 15.0 m)
Now, you can calculate the net work done on the wagon.