You can crack a coconut in this oversized cracker. The apparatus is set across the main demonstration table in the lecture hall. The C-clamp shown at right holds the tab at the hinge end to the table top to keep it from rising when you use the cracker. For maximum leverage, you can pull the handle out until the lip at the end stops against the loop in the top of the cracker. The clamp across the bottom member of the cracker prevents the coconut from sliding forward when you pull down on the handle. (The coconut is drilled and drained before class time to prevent the mess that would otherwise result when you cracked the coconut.)
This apparatus is an example of a lever, in which the fulcrum, in this case the pivot or hinge, is at one end, you apply the operating force, or effort, at the opposite end, and the load, that is, the force you must overcome to operate the lever, is somewhere between them. This is often called a “class two” lever. In the apparatus as shown above, when you pull down on the handle, you exert a counterclockwise torque (pointing towards the front through the pivot pin), and the coconut exerts a clockwise torque (pointing rearwards through the pivot pin). We can express these as τ = r × F, where r is the displacement vector from the pivot to your hand or to the coconut, and F is the force applied by your hand or by the coconut, respectively. When you pull down on the handle, as long as these torques balance, nothing happens. When the torque you apply exceeds the torque that the coconut can provide, that is, when the force on the coconut exceeds what the coconut can sustain, the coconut breaks.
The distance between the hinge and the contact point of the coconut and the lever is about 29 cm. The length of the handle from the hinge to the end is about 157 cm. Assuming you place your hand at the very end, taking 5 cm as roughly half a handbreadth, we can take your lever arm as about 152 cm. If you extend the handle fully, its overall length is about 213 cm, for a lever arm of about 208 cm. The moment that the coconut has is thus its maximum compressive force multiplied by 0.29 m, and your moment is the force you apply multiplied by 1.52 m, or 2.08 m if you extend the handle all the way. The moment is r(F sin θ), the component of F that is perpendicular to the handle, or (r sin θ) F, the component of the displacement along the handle that is perpendicular to F. The force the coconut applies is perpendicular to the handle. Even though you can pull in a direction that is perpendicular to the handle, gravity pulls straight down on you. Because the handle is not quite horizontal, your moment is reduced by the magnitude of the component of your weight that lies along the handle. Still, if we estimate the angle of the handle as shown in the photograph as about 30°, the component of your weight that you can apply is sin(60°) = 0.866 times it. The coconut’s moment, then, is just rF, and as long as you are not pulling with more than 0.866 times your weight, yours is also rF, where r and F are the respective distances from the pivot, and forces. Its units are N·m. When you pull down on the handle, then, the coconut experiences a force that is anywhere from about 1.5/0.29 = 5.2 to 2.1/0.29 = 7.2 times the force that you apply to the handle. If you stood on the coconut, it could support your weight without breaking. When you put it in the coconut cracker, though, you can apply as much as five to seven times your weight to it, depending on how far you extend the handle, and on how hard you pull downward. At some point, the force the coconut must provide to resist the force you apply to it by means of the cracker, exceeds its breaking force, and the coconut shatters.
What about the pivot?
It is interesting to note what force the pivot experiences as you operate the coconut cracker. From your perspective, it is the fulcrum, and the coconut is the load. From the perspective of the pivot, the coconut is the fulcrum, and the pivot is trying to operate a class one lever (see demonstration 20.03, 28.06 or 32.03 – Lever arm) against the force (load) that you apply. Your moment about the coconut is the distance between it and your hand, or from (1.5 - 0.29) = 1.2 m to (2.1 - 0.29) = 1.8 m times the force you apply. The moment arm the pivot has, though, is just the 0.29-m distance between it and the coconut. So the pivot must provide anywhere from 1.2/0.29 = 4.1 to 1.8/0.29 = 6.2 times the force that you apply to the handle. So if, for example, with the handle fully extended, you pull down on it with 100 pounds (445 N, which you can do if you weigh at least 116 (= 100/0.866) pounds (514 N)), the coconut feels 720 pounds (3,200 N), and the pivot must withstand 620 pounds (2,760 N) – a significant portion of the force applied to the coconut. Just how great a force the pivot must exert depends on how much the coconut can withstand before it breaks. Also, the less you extend the handle, the smaller the force at the pivot, though perhaps not by much. To exert a force of 720 pounds (3,200 N) on the coconut with the handle as shown in the photograph, you must pull down with 100(2.08/1.52) = 137 pounds (610 N). The pivot feels 4.1 × 137 = 561 pounds (2,500 N), still a significant portion of what the coconut experiences, but somewhat less than in the first case, because its moment arm, relative to your moment arm, is greater than in the first case.
References:
1) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 231-233.