You're pulling a wagon with a child in it and we want to find out how much work you're doing.
First, let's understand what work is. In physics, work is the energy transferred to or from an object when a force is applied to it and the object moves. The formula for work (W) is:
W = F * d * cos(θ),
where
- W is the work done,
- F is the force applied,
- d is the distance over which the force is applied, and
- θ (theta) is the angle between the force and the direction of movement.
In your example, you're pulling the wagon with a tension of 20 N in the handle, you're pulling it 170 m, and the angle between the handle and the ground is 60 degrees.
So, let's plug the numbers into the formula:
W = 20 N * 170 m * cos(60°).
Now, let's break this down even more.
1. Force (F): The force you're applying is the tension in the handle, which is 20 N (Newtons).
2. Distance (d): You're pulling the wagon for 170 m (meters), so that's the distance over which you're applying the force.
3. Angle (θ): The angle between the handle and the direction you're pulling is 60 degrees. When the angle is 0 degrees, the force is directly in the direction of movement, and when it's 90 degrees, the force is perpendicular to the direction of movement. At 60 degrees, the force is somewhere in between.
Now, cos(60°) is equal to 0.5. You can find this value using a calculator or trigonometry table. Let's plug this value into the equation:
W = 20 N * 170 m * 0.5
= 20 * 170 * 0.5
= 3400 * 0.5
= 1700 Joules.
So, you do 1700 Joules of work pulling the wagon.
In simpler words, because you are pulling the wagon at an angle, not all of your force is used to move it in the direction you want. Only half of your force is actually pulling it forward, and this results in doing 1700 Joules of work.