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a wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. a force is applied in the direction 0, 4, −3 at the end of the wrench. find the magnitude of the force needed to supply 130 n · m of torque to the bolt. (round your answer to the nearest whole number.)

Answer :

The magnitude of force required to apply 130 n.m of torque to the bolt is 722.

f = magnitude of force

F = Vector force.

F =  f [(0 i + 4 j - 3 k)] (02 + 42 + (-3)2)) = (f/5) (4 j - 3 k)

r = 30 cm = 0.30 m

[tex]\tau[/tex] = Torque = 130

Using the formula

[tex]\tau[/tex] = r x F

130 = (0.30 j) x (f/5) (4 j - 3 k)

130 = (f/5) (-0.9 i)

f = 130 x 5 /0.9 = 722

Hence, 722 is the magnitude of the force needed to supply 130 n.m of torque to the bolt.

What do you mean by the magnitude of force?

  • The magnitude of force is the measure of how strong an impact a physical force has.
  • This can be used in many different situations, such as when you are determining whether or not someone is injured.
  • The police use this measurement to determine if they need to call for backup or evacuate the scene.
  • It is also used in engineering and construction to calculate the amount of pressure that needs to be applied in order for a structure to withstand damage.

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