Exam I, PHY-215, Fall 2017, Date: 10-9-2017 ID # Name planet X. They performed a

Question

Exam I, PHY-215, Fall 2017, Date: 10-9-2017 ID # Name planet X. They performed a series of experiments A group of astronauts found a new planet which they named there using same apparatus that you have used in your last three labs as follows: Free Fall Experiment 30%) They first performed the free fall experiment and found the follow ing plot after plotting height squared, where height was measured in meters and time in seconds: vs time 700 6.0038x+2.064 600 300 200 100 0 20 40 6 80 100 120 Figure 1: Height versus time squared for a free-fall experiment. Answer all the questions and show all your work I. What is the slope of the best fit line? 2. What is the initial height of the object? 4,0 3. What is the gravitational acceleration (is) of the Planet X? Explain how you obtained your answer 4. If an object is dropped from 10m, how much time it will take to hit the surface of this planet? 5. If the same object is dropped from 10m on the earth would it take more or less time ? After they found the gravitational acceleration (g they examined the vector addition formula in this Planet X using a force table (same as your experiment #3). The following table shows the relevant data used for the hanging masses amd their directions Direction (o 30 150 Vecter Mass (g) 50 Answer the following questions (Show all your work!): 6. What are the weights of the hanging masses in this planet X? 7. Using the component method, what are the x- and y components of vectors Fi and F2? 8. Using the component method, what is the magnitude and direction of the resulting vector: R? Now consider that the position of the masses are switched; F is replaced by F, and F, is replaced by F, How will R be affected? a) Both magnitude and direction of R will change b) Magnitude of R will change but its direction will remain the same. c) Magnitunde will be the same but the direction will change d) Nothing at all.

Explanation / Answer

given graph

equation, y = 6.0038x + 2.064

R^2 = 0.9998

1. slope of the best fit line from the equation of the line is m

whenre y = mx + c

comparing with the equation from the graph

slope, m = 6.0038

2. the kinematic equation of free fall is givne by

y = yo - 0.5at^2

so initial height of the object = yo = 2.064 m

3. acceleration due to gravity on the planet, a

comparing two equations

0.5a = -m

a = -2m = -12.0076 m/s/s pointing downwards)

4. given initial height = h = 10 m

time taken to reach surface = t

initial speed = 0

hence

h = 0.5at^2

10 = 0.5*12.0076*t^2

t = 1.29 s

5. on earth, time taken will be

10 = 0.5*9.81*t^2

t = 1.427 s

hence on earth the object wsill take more time to reach the surface when dropped from the same height

6. mass = 50 g = 0.05 kg

weight = 0.05*12.0076 = 0.60038 N

mass = 200 g = 0.2 kg

weight = 0.2*12.0076 = 2.40152 N

7. given |F1| = 0.60038 N

angle = 30 deg

so x compoennt = F1x = |F1|cos(30) = 0.5199 N

so y compoennt = F1y = |F1|sin(30) = 0.30019 N

given |F2| = 2.40152 N

angle = 150 deg

so x compoennt = F2x = |F2|cos(150) = -2.0797 N

so y compoennt = F2y = |F2|sin(150) = 1.20076 N

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