The same push on the longer bar snapped the bolt

# Self-authored for the EML case corpus (no external origin). A mechanic frees a
# seized nut with a 75 cm bar, then tightens the new bolt with the same bar and
# the same firm push used every day on a 25 cm wrench - a push that always gives
# the specified 100 newton-metres. How tight the bolt really goes is computed
# below.
#
# The reasoning is careful. The push really is the same 400 newtons, a trained
# feel; on the usual wrench it really does give the specified tightness; the
# bolt really is the right bolt; and the intent is exactly 'tighten to spec'.
#
# Tightness is torque, the push times the distance from the bolt to where it is
# applied. Three times the lever with the same push is three times the torque:
# 300 newton-metres on a bolt that yields at 120. The push that would have given
# the specified 100 on the long bar is a third of the usual one, 133 newtons.

400 => push_newtons
25 => usual_wrench_cm
75 => long_bar_cm
100 => specified_torque_nm
120 => bolt_yields_at_nm

int(push_newtons * usual_wrench_cm / 100) => torque_on_the_usual_wrench_nm
int(push_newtons * long_bar_cm / 100) => torque_on_the_long_bar_nm
int(long_bar_cm / usual_wrench_cm) => lever_times_longer
torque_on_the_long_bar_nm - bolt_yields_at_nm => over_the_yield_nm
int(torque_on_the_long_bar_nm * 100 / bolt_yields_at_nm) => torque_vs_yield_percent
int(specified_torque_nm * 100 / long_bar_cm) => push_for_spec_on_the_long_bar_newtons

"push                            : " + str(push_newtons) + " N" ^0
"usual wrench                    : " + str(usual_wrench_cm) + " cm, torque " + str(torque_on_the_usual_wrench_nm) + " N-m, the specified " + str(specified_torque_nm) ^0
"long bar                        : " + str(long_bar_cm) + " cm, " + str(lever_times_longer) + " times the lever, torque " + str(torque_on_the_long_bar_nm) + " N-m" ^0
"bolt yields at                  : " + str(bolt_yields_at_nm) + " N-m; long bar is " + str(over_the_yield_nm) + " over, " + str(torque_vs_yield_percent) + " percent of it" ^0
"push for spec on the long bar   : " + str(push_for_spec_on_the_long_bar_newtons) + " N" ^0
"" ^0

# ---- what the mechanic verified ----

"the same-push reasoning" ^0
"  push : " + str(push_newtons) + " N, a trained, repeatable feel" ^0
"  on the usual wrench : exactly the specified " + str(specified_torque_nm) + " N-m" ^0
"  bolt : the right one" ^0
"  intent : tighten to spec" ^0
"  facts wrong : 0" ^0
"  verdict : THE USUAL PUSH GIVES THE USUAL TIGHTNESS" ^0
"" ^0
"  keeping the push the same is the part done right here, and it" ^0
"  is why " + str(push_newtons) + " N is exactly what reached the handle" ^0
"" ^0

# ---- what the lever does ----

"torque is push times lever" ^0
"  what tightens a bolt : the turning effect, push times the" ^0
"    distance from the bolt" ^0
"  usual wrench : " + str(push_newtons) + " N at " + str(usual_wrench_cm) + " cm, " + str(torque_on_the_usual_wrench_nm) + " N-m" ^0
"  long bar : the same " + str(push_newtons) + " N at " + str(long_bar_cm) + " cm, " + str(torque_on_the_long_bar_nm) + " N-m" ^0
"  what the trained feel measured : the push, which the hand can" ^0
"    feel; not the lever, which it cannot" ^0
"" ^0

# ---- what the mechanic got ----

"the bolt" ^0
"  believed : " + str(specified_torque_nm) + " N-m, to spec" ^0
"  actual : " + str(torque_on_the_long_bar_nm) + " N-m, past its yield of " + str(bolt_yields_at_nm) + ", stretched and snapped" ^0
"  was the push different : no; " + str(push_newtons) + " N both times" ^0
"  is the push the tightness : only on the lever it was learned on" ^0
"" ^0

# ---- null control ----

# The same bolt tightened by torque instead of by the feel of the push.
100 => nc_torque_read_from_the_push_nm
300 => nc_torque_read_from_push_times_lever_nm
200 => nc_nm_the_long_lever_adds

"null control - count the lever" ^0
"  torque, read from the push : " + str(nc_torque_read_from_the_push_nm) + " N-m" ^0
"  torque, read from push times lever : " + str(nc_torque_read_from_push_times_lever_nm) + " N-m" ^0
"  N-m the long lever adds : " + str(nc_nm_the_long_lever_adds) ^0
"  no bolt and no push changed; the turning effect was computed" ^0
"  from both of its factors" ^0
"" ^0

# ---- the rule ----

"what the same trained push guarantees" ^0
"  the same force reaches the handle : exactly, " + str(push_newtons) + " N" ^0
"  the bolt reaches the same tightness : not addressed; torque is" ^0
"    push times lever, the bar is " + str(lever_times_longer) + " times the wrench, and the bolt" ^0
"    gets " + str(torque_on_the_long_bar_nm) + " N-m against a yield of " + str(bolt_yields_at_nm) ^0
"" ^0

"a feel for force is a feel for one lever; change the lever and the same" ^0
"hand is a different tool" ^0
"" ^0

"The push was the usual " + str(push_newtons) + " N - exactly. But torque is push times lever, and the" ^0
"bar is " + str(lever_times_longer) + " times the wrench, so the bolt got " + str(torque_on_the_long_bar_nm) + " N-m against a yield of " + str(bolt_yields_at_nm) + ", where" ^0
"" + str(push_for_spec_on_the_long_bar_newtons) + " N would have given the specified " + str(specified_torque_nm) + ", until the tightness is set by torque and" ^0
"not by the feel of the push." ^0

push_newtons = 400
usual_wrench_cm = 25
long_bar_cm = 75
specified_torque_nm = 100
bolt_yields_at_nm = 120
torque_on_the_usual_wrench_nm = int(push_newtons * usual_wrench_cm / 100)
torque_on_the_long_bar_nm = int(push_newtons * long_bar_cm / 100)
lever_times_longer = int(long_bar_cm / usual_wrench_cm)
over_the_yield_nm = torque_on_the_long_bar_nm - bolt_yields_at_nm
torque_vs_yield_percent = int(torque_on_the_long_bar_nm * 100 / bolt_yields_at_nm)
push_for_spec_on_the_long_bar_newtons = int(specified_torque_nm * 100 / long_bar_cm)
print("push                            : " + str(push_newtons) + " N")
print("usual wrench                    : " + str(usual_wrench_cm) + " cm, torque " + str(torque_on_the_usual_wrench_nm) + " N-m, the specified " + str(specified_torque_nm))
print("long bar                        : " + str(long_bar_cm) + " cm, " + str(lever_times_longer) + " times the lever, torque " + str(torque_on_the_long_bar_nm) + " N-m")
print("bolt yields at                  : " + str(bolt_yields_at_nm) + " N-m; long bar is " + str(over_the_yield_nm) + " over, " + str(torque_vs_yield_percent) + " percent of it")
print("push for spec on the long bar   : " + str(push_for_spec_on_the_long_bar_newtons) + " N")
print("")
print("the same-push reasoning")
print("  push : " + str(push_newtons) + " N, a trained, repeatable feel")
print("  on the usual wrench : exactly the specified " + str(specified_torque_nm) + " N-m")
print("  bolt : the right one")
print("  intent : tighten to spec")
print("  facts wrong : 0")
print("  verdict : THE USUAL PUSH GIVES THE USUAL TIGHTNESS")
print("")
print("  keeping the push the same is the part done right here, and it")
print("  is why " + str(push_newtons) + " N is exactly what reached the handle")
print("")
print("torque is push times lever")
print("  what tightens a bolt : the turning effect, push times the")
print("    distance from the bolt")
print("  usual wrench : " + str(push_newtons) + " N at " + str(usual_wrench_cm) + " cm, " + str(torque_on_the_usual_wrench_nm) + " N-m")
print("  long bar : the same " + str(push_newtons) + " N at " + str(long_bar_cm) + " cm, " + str(torque_on_the_long_bar_nm) + " N-m")
print("  what the trained feel measured : the push, which the hand can")
print("    feel; not the lever, which it cannot")
print("")
print("the bolt")
print("  believed : " + str(specified_torque_nm) + " N-m, to spec")
print("  actual : " + str(torque_on_the_long_bar_nm) + " N-m, past its yield of " + str(bolt_yields_at_nm) + ", stretched and snapped")
print("  was the push different : no; " + str(push_newtons) + " N both times")
print("  is the push the tightness : only on the lever it was learned on")
print("")
nc_torque_read_from_the_push_nm = 100
nc_torque_read_from_push_times_lever_nm = 300
nc_nm_the_long_lever_adds = 200
print("null control - count the lever")
print("  torque, read from the push : " + str(nc_torque_read_from_the_push_nm) + " N-m")
print("  torque, read from push times lever : " + str(nc_torque_read_from_push_times_lever_nm) + " N-m")
print("  N-m the long lever adds : " + str(nc_nm_the_long_lever_adds))
print("  no bolt and no push changed; the turning effect was computed")
print("  from both of its factors")
print("")
print("what the same trained push guarantees")
print("  the same force reaches the handle : exactly, " + str(push_newtons) + " N")
print("  the bolt reaches the same tightness : not addressed; torque is")
print("    push times lever, the bar is " + str(lever_times_longer) + " times the wrench, and the bolt")
print("    gets " + str(torque_on_the_long_bar_nm) + " N-m against a yield of " + str(bolt_yields_at_nm))
print("")
print("a feel for force is a feel for one lever; change the lever and the same")
print("hand is a different tool")
print("")
print("The push was the usual " + str(push_newtons) + " N - exactly. But torque is push times lever, and the")
print("bar is " + str(lever_times_longer) + " times the wrench, so the bolt got " + str(torque_on_the_long_bar_nm) + " N-m against a yield of " + str(bolt_yields_at_nm) + ", where")
print("" + str(push_for_spec_on_the_long_bar_newtons) + " N would have given the specified " + str(specified_torque_nm) + ", until the tightness is set by torque and")
print("not by the feel of the push.")

push                            : 400 N
usual wrench                    : 25 cm, torque 100 N-m, the specified 100
long bar                        : 75 cm, 3 times the lever, torque 300 N-m
bolt yields at                  : 120 N-m; long bar is 180 over, 250 percent of it
push for spec on the long bar   : 133 N

the same-push reasoning
  push : 400 N, a trained, repeatable feel
  on the usual wrench : exactly the specified 100 N-m
  bolt : the right one
  intent : tighten to spec
  facts wrong : 0
  verdict : THE USUAL PUSH GIVES THE USUAL TIGHTNESS

  keeping the push the same is the part done right here, and it
  is why 400 N is exactly what reached the handle

torque is push times lever
  what tightens a bolt : the turning effect, push times the
    distance from the bolt
  usual wrench : 400 N at 25 cm, 100 N-m
  long bar : the same 400 N at 75 cm, 300 N-m
  what the trained feel measured : the push, which the hand can
    feel; not the lever, which it cannot

the bolt
  believed : 100 N-m, to spec
  actual : 300 N-m, past its yield of 120, stretched and snapped
  was the push different : no; 400 N both times
  is the push the tightness : only on the lever it was learned on

null control - count the lever
  torque, read from the push : 100 N-m
  torque, read from push times lever : 300 N-m
  N-m the long lever adds : 200
  no bolt and no push changed; the turning effect was computed
  from both of its factors

what the same trained push guarantees
  the same force reaches the handle : exactly, 400 N
  the bolt reaches the same tightness : not addressed; torque is
    push times lever, the bar is 3 times the wrench, and the bolt
    gets 300 N-m against a yield of 120

a feel for force is a feel for one lever; change the lever and the same
hand is a different tool

The push was the usual 400 N - exactly. But torque is push times lever, and the
bar is 3 times the wrench, so the bolt got 300 N-m against a yield of 120, where
133 N would have given the specified 100, until the tightness is set by torque and
not by the feel of the push.

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