nail is hammered into a board so that it would take a force, applied straight up

Question

nail is hammered into a board so that it would take a force, applied straight upward on the head of the nail, to pull it out. (Take an upward force to be positive.) A carpenter uses a crowbar to try to pry it out. The length of the handle of the crowbar is , and the length of the forked portion of the crowbar (which fits around the nail) is . Assume that the forked portion of the crowbar is perfectly horizontal. The handle of the crowbar makes an-angle with the horizontal, and the carpenter pulls directly along the horizontal. Part A With what force must the carpenter pull on the crowbar to remove the nail? Express the force in terms of F_nail, L_h, L_n, and theta. Part B What is the magnitude of the normal force that the surface exerts on the crowbar, ? Express your answer for the normal force in terms of F_nail, L_h, L_n, and theta. Take the upward direction to be positive. Three bars are shown in the figure. Both bars A and B have acting on them in the horizontal direction. Bar C has strictly perpendicular to the bar. , , and are the same quantities in each case. Part C Let the magnitude of the torque about the bend in the crowbars be denoted t_a, t_b, and t_c and for each of the three cases shown. Which of the following is the correct relationship between the magnitude of of the torques? Please show detailed work. I know part A is supposed to be f_pull= (F_nail*L_n)/sin(theta)L_h Part B is supposed to be F_bar=(f_pullsin(theta)L_h)/L_n Part C is supposed to be t_a < t_b = t_c

Explanation / Answer

A nail is hammered into a board so that it would take a force F_nail, applied straight upward on the head of the nail, to pull it out. (Take an upward force to be positive.) A carpenter uses a crowbar to try to pry it out. The length of the handle of the crowbar is L_h, and the length of the forked portion of the crowbar (which fits around the nail) is L_n. Assume that the forked portion of the crowbar is perfectly horizontal. The handle of the crowbar makes an angle theta with the horizontal, and the carpenter pulls directly along the horizontal. With what force F_pull must the carpenter pull on the crowbar to remove the nail? Express the force in terms of F_nail, L_h, L_n, and theta. If the handle was perpendicular to the forked portion, the torque would equal F pull * L handle. Since the handle of the crowbar makes an angle ? with the horizontal, the component of the length of the handle which is perpendicular to the horizontal forked portion = L * sin ? Torque = F pull * L_h * sin ? The horizontal forked portion is perpendicular to the nail, so the torque caused by the forked portion pulling the nail = F_nail * L_n F pull * L_h * sin ? = F_nail * L_n F pull = (F_nail * L_n) ÷ (L_h * sin ?) Now, imagine that F_pull is not large enough to dislodge the nail. In other words, the nail stays in place, and, if the surface below the crowbar weren't present, the crowbar would rotate around the point of contact with the nail. This makes it natural to take the pivot point to be the point where the crowbar is in contact with the nail. (But you are always free to choose the pivot point to be any fixed point, even one some distance from the object.) F_pull ........ ? ........ ..... ! .......... ... ! .............. .! ...........__ ! ........ I ....? F normal I choose pivot point at nail! What is the magnitude of the normal force that the surface exerts on the crowbar, F_bar? As you attempt to remove the nail, the point where the crow bends is pushing down on the surface. So the normal force that the surface exerts UP on the crowbar, is equal to the force that the point at the bend of the crow bar is pushing DOWN. This force causes clockwise torque around the pivot point. Counter clockwise torque = F pull * L_h * sin ? clockwise torque = F normal * L_n F normal * L_n = F pull * L_h * sin ? F normal = (F pull * L_h * sin ?) ÷ L_n

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.