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A space explorer lands on an unknown planet. She decides to measure the gravitational acceleration by tying a rock to the end of a 1.5 m string and using it as a pendulum. She pulls the rock 0.1 m to the right (as shown) and lets go. The pendulum swings with a period of 1.0 s. Assume positive-x is to the right, and x = 0 when the string is vertical. The diagram shows the pendulum at time t = 0. (For example, please write 3.14 instead of, or 1.41 instead of √2, etc) a) What is the angular frequency, w? write all your final numerical answers using two decimal places. b) What is the gravitational acceleration of the planet, g? .5m 0.1m c) Write an expression for the horizontal position of the rock as a function of time, x(t). All terms should be evaluated numerically (except t). d) Calculate the maximum horizontal acceleration of the rock. e) Draw a diagram of the pendulum when the rock has the maximum positive acceleration. f) Having measured g, the explorer now wants to use the pendulum to find the mass of the rock. Can she do this? If so, how? If not, why not? Briefly explain your answer, no calculations required! g) Using forces, briefly explain why the pendulum swings back and forth (simple harmonic motion).

A space explorer lands on an unknown planet. She decides to measure the gravitational acceleration by tying a rock to the end of a 1.5 m string and using it as a pendulum. She pulls the rock 0.1 m to the right (as shown) and lets go. The pendulum swings with a period of 1.0 s. Assume positive-x is to the right, and x = 0 when the string is vertical. The diagram shows the pendulum at time t = 0. (For example, please write 3.14 instead of, or 1.41 instead of √2, etc) a) What is the angular frequency, w? write all your final numerical answers using two decimal places. b) What is the gravitational acceleration of the planet, g? .5m 0.1m c) Write an expression for the horizontal position of the rock as a function of time, x(t). All terms should be evaluated numerically (except t). d) Calculate the maximum horizontal acceleration of the rock. e) Draw a diagram of the pendulum when the rock has the maximum positive acceleration. f) Having measured g, the explorer now wants to use the pendulum to find the mass of the rock. Can she do this? If so, how? If not, why not? Briefly explain your answer, no calculations required! g) Using forces, briefly explain why the pendulum swings back and forth (simple harmonic motion).

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Please use A,B,C answers as they are completed, only need help with D,E,F,G. Thank you!

a) Angular Frequency W = 27 2F T W = 2X W = 6.281a2/5 B) gravitational acceleration T = 2^ 2x √5 + 1 = 1.5m T=15e= F) Yes/No 1=2X √5 - 15 1 4^² g 9 = (1.5) x 4x² 9=5715 M/S² 2) Maximum acceleration () equation of motion x (t) = Acos (wt) (x) (€) = 0.1 cos (6.286) E) Diagram of Pendulam
Transcribed Image Text:a) Angular Frequency W = 27 2F T W = 2X W = 6.281a2/5 B) gravitational acceleration T = 2^ 2x √5 + 1 = 1.5m T=15e= F) Yes/No 1=2X √5 - 15 1 4^² g 9 = (1.5) x 4x² 9=5715 M/S² 2) Maximum acceleration () equation of motion x (t) = Acos (wt) (x) (€) = 0.1 cos (6.286) E) Diagram of Pendulam
A space explorer lands on an unknown planet. She decides to measure the gravitational acceleration by tying a rock to the end of a 1.5 m string and using it as a pendulum. She pulls the rock 0.1 m to the right (as shown) and lets go. The pendulum swings with a period of 1.0 s. Assume positive-x is to the right, and x = 0 when the string is vertical. The diagram shows the pendulum at time t = 0. (For example, please write 3.14 instead of л, or 1.41 instead of √2, etc) a) What is the angular frequency, w? write all your final numerical answers using two decimal places. b) What is the gravitational acceleration of the planet, g? 1.5m 0.1m c) Write an expression for the horizontal position of the rock as a function of time, x(t). All terms should be evaluated numerically (except t). d) Calculate the maximum horizontal acceleration of the rock. e) Draw a diagram of the pendulum when the rock has the maximum positive acceleration. f) Having measured g, the explorer now wants to use the pendulum to find the mass of the rock. Can she do this? If so, how? If not, why not? Briefly explain your answer, no calculations required! g) Using forces, briefly explain why the pendulum swings back and forth (simple harmonic motion).
Transcribed Image Text:A space explorer lands on an unknown planet. She decides to measure the gravitational acceleration by tying a rock to the end of a 1.5 m string and using it as a pendulum. She pulls the rock 0.1 m to the right (as shown) and lets go. The pendulum swings with a period of 1.0 s. Assume positive-x is to the right, and x = 0 when the string is vertical. The diagram shows the pendulum at time t = 0. (For example, please write 3.14 instead of л, or 1.41 instead of √2, etc) a) What is the angular frequency, w? write all your final numerical answers using two decimal places. b) What is the gravitational acceleration of the planet, g? 1.5m 0.1m c) Write an expression for the horizontal position of the rock as a function of time, x(t). All terms should be evaluated numerically (except t). d) Calculate the maximum horizontal acceleration of the rock. e) Draw a diagram of the pendulum when the rock has the maximum positive acceleration. f) Having measured g, the explorer now wants to use the pendulum to find the mass of the rock. Can she do this? If so, how? If not, why not? Briefly explain your answer, no calculations required! g) Using forces, briefly explain why the pendulum swings back and forth (simple harmonic motion).
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