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Sitting on a Cantilever If you have had class in D101 SCI, then you would have been sitting on a cantilever. The chair is connected to the concrete with two bolts while the person's body weight hangs off the chair about \( 30 \mathrm{~cm} \) from the base with no direct support under it. The problem: The chair and person have a combined mass of \( 100 \mathrm{~kg} \) and their weight acts \( 30 \mathrm{~cm} \) from the base. Two bolts which are screwed into the concrete are \( 20 \mathrm{~cm} \) apart. We will assume each bolt exerts and upward force to support half the combined weight ( \( 50 \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s} / \mathrm{s} \) ) equal to \( 490 \mathrm{~N} \). In addition to providing an upward force, the bolts also provide horizontal forces that are different in size. a) Draw a force diagram. Show the force provided by each bolt as both a horizontal force and a vertical force. If the size of the forces is known, indicate it on the diagram. If the size of the force is unknown, label the force with a variable. Assume the bolt exerts a force to the right and the bottom bolt exerts a force to the left. b) Using your force diagram, write the 3 equations for static equilibrium (balance torques, balance \( x \)-forces, and balanced \( y \)-forces) specific to this problem. Your equations will have unknown variables in them. c) Solve your equations in part b to determine the size and direction of the force provided by each bolt. d) One of the bolts does not actually hold the base to the concrete, meaning you could remove the bolt and the chair would not fall down, which one is it? Does your calculation agree? But this bolt is important because it does support half the weight.

          Sitting on a Cantilever

If you have had class in D101 SCI, then you would have been sitting on a cantilever. The chair is connected to the concrete with two bolts while the person's body weight hangs off the chair about \( 30 \mathrm{~cm} \) from the base with no direct support under it.

The problem: The chair and person have a combined mass of \( 100 \mathrm{~kg} \) and their weight acts \( 30 \mathrm{~cm} \) from the base. Two bolts which are screwed into the concrete are \( 20 \mathrm{~cm} \) apart. We will assume each bolt exerts and upward force to support half the combined weight ( \( 50 \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s} / \mathrm{s} \) ) equal to \( 490 \mathrm{~N} \). In addition to providing an upward force, the bolts also provide horizontal forces that are different in size.
a) Draw a force diagram. Show the force provided by each bolt as both a horizontal force and a vertical force. If the size of the forces is known, indicate it on the diagram. If the size of the force is unknown, label the force with a variable. Assume the bolt exerts a force to the right and the bottom bolt exerts a force to the left.
b) Using your force diagram, write the 3 equations for static equilibrium (balance torques, balance \( x \)-forces, and balanced \( y \)-forces) specific to this problem. Your equations will have unknown variables in them.
c) Solve your equations in part b to determine the size and direction of the force provided by each bolt.
d) One of the bolts does not actually hold the base to the concrete, meaning you could remove the bolt and the chair would not fall down, which one is it? Does your calculation agree? But this bolt is important because it does support half the weight.

Sitting on a Cantilever

If you have had class in D101 SCI, then you would have been sitting on a cantilever. The chair is connected to the concrete with two bolts while the person's body weight hangs off the chair about 30 cm from the base with no direct support under it.

The problem: The chair and person have a combined mass of 100 kg and their weight acts 30 cm from the base. Two bolts which are screwed into the concrete are 20 cm apart. We will assume each bolt exerts and upward force to support half the combined weight ( 50 kg× 9.8 m / s / s ) equal to 490 N. In addition to providing an upward force, the bolts also provide horizontal forces that are different in size.
a) Draw a force diagram. Show the force provided by each bolt as both a horizontal force and a vertical force. If the size of the forces is known, indicate it on the diagram. If the size of the force is unknown, label the force with a variable. Assume the bolt exerts a force to the right and the bottom bolt exerts a force to the left.
b) Using your force diagram, write the 3 equations for static equilibrium (balance torques, balance x-forces, and balanced y-forces) specific to this problem. Your equations will have unknown variables in them.
c) Solve your equations in part b to determine the size and direction of the force provided by each bolt.
d) One of the bolts does not actually hold the base to the concrete, meaning you could remove the bolt and the chair would not fall down, which one is it? Does your calculation agree? But this bolt is important because it does support half the weight.

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