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You are part of a team to help design the atrium of a new building. Your boss wants to suspend a sculpture of mass m, high over the room by hanging it from the ceiling using thin, clear string so that it will be difficult to see how the sculpture is held up. The string she wants to use is specified to be able to support a vertically hanging mass of m. To be safe, she suggests attaching two lines to the sculpture. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has line 1 attaching to the left-hand-side of the sculpture, making an angle of 8, with the ceiling. The other line, line 2, attaches to the right-hand-side of the sculpture and makes an angle of 02 with the ceiling. She knows you are taking physics so she asks you if her design would work. a. Make a sketch of the hanging sculpture. Label angles and which line is 1 and 2. b. Draw a free body diagram for the sculpture. Remember, tension forces always pull (they cannot push). c. Write a Newton's 2nd Law equation for the sculpture. d. Use your Newton's 2nd Law equation to find an expression for the norm of the force of tension in line 1. Your answer should be a vector expression that only contains m, 61, 02, and g. e. If 01 = 02 = 0, what would be the smallest angle 6 that you could recommend as safe? Explain your reasoning.

You are part of a team to help design the atrium of a new building. Your boss wants to suspend a sculpture of mass m, high over the room by hanging it from the ceiling using thin, clear string so that it will be difficult to see how the sculpture is held up. The string she wants to use is specified to be able to support a vertically hanging mass of m. To be safe, she suggests attaching two lines to the sculpture. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has line 1 attaching to the left-hand-side of the sculpture, making an angle of 8, with the ceiling. The other line, line 2, attaches to the right-hand-side of the sculpture and makes an angle of 02 with the ceiling. She knows you are taking physics so she asks you if her design would work. a. Make a sketch of the hanging sculpture. Label angles and which line is 1 and 2. b. Draw a free body diagram for the sculpture. Remember, tension forces always pull (they cannot push). c. Write a Newton's 2nd Law equation for the sculpture. d. Use your Newton's 2nd Law equation to find an expression for the norm of the force of tension in line 1. Your answer should be a vector expression that only contains m, 61, 02, and g. e. If 01 = 02 = 0, what would be the smallest angle 6 that you could recommend as safe? Explain your reasoning.

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You are part of a team to help design the atrium of a new building. Your boss wants to suspend a sculpture of mass \( m \), high over the room by hanging it from the ceiling using thin, clear string so that it will be difficult to see how the sculpture is held up. The string she wants to use is specified to be able to support a vertically hanging mass of \( m \). To be safe, she suggests attaching two lines to the sculpture. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has line 1 attaching to the left-hand-side of the sculpture, making an angle of \( \theta_1 \) with the ceiling. The other line, line 2, attaches to the right-hand-side of the sculpture and makes an angle of \( \theta_2 \) with the ceiling. She knows you are taking physics so she asks you if her design would work. a. Make a sketch of the hanging sculpture. Label angles and which line is 1 and 2. b. Draw a free body diagram for the sculpture. Remember, tension forces always pull (they cannot push). c. Write a Newton’s 2\(^\text{nd}\) Law equation for the sculpture. d. Use your Newton’s 2\(^\text{nd}\) Law equation to find an expression for the norm of the force of tension in line 1. Your answer should be a vector expression that only contains \( m, \theta_1, \theta_2, \) and \( g \). e. If \( \theta_1 = \theta_2 = \theta \), what would be the smallest angle \( \theta \) that you could recommend as safe? Explain your reasoning.
Transcribed Image Text:You are part of a team to help design the atrium of a new building. Your boss wants to suspend a sculpture of mass \( m \), high over the room by hanging it from the ceiling using thin, clear string so that it will be difficult to see how the sculpture is held up. The string she wants to use is specified to be able to support a vertically hanging mass of \( m \). To be safe, she suggests attaching two lines to the sculpture. Each line would come from the opposite side of the ceiling to attach to the hanging sculpture. Her initial design has line 1 attaching to the left-hand-side of the sculpture, making an angle of \( \theta_1 \) with the ceiling. The other line, line 2, attaches to the right-hand-side of the sculpture and makes an angle of \( \theta_2 \) with the ceiling. She knows you are taking physics so she asks you if her design would work. a. Make a sketch of the hanging sculpture. Label angles and which line is 1 and 2. b. Draw a free body diagram for the sculpture. Remember, tension forces always pull (they cannot push). c. Write a Newton’s 2\(^\text{nd}\) Law equation for the sculpture. d. Use your Newton’s 2\(^\text{nd}\) Law equation to find an expression for the norm of the force of tension in line 1. Your answer should be a vector expression that only contains \( m, \theta_1, \theta_2, \) and \( g \). e. If \( \theta_1 = \theta_2 = \theta \), what would be the smallest angle \( \theta \) that you could recommend as safe? Explain your reasoning.
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