5. A simple pendulum has a 150.0 g mass tied to it and 28.00 seconds are require

Question

5. A simple pendulum has a 150.0 g mass tied to it and 28.00 seconds are required to complete 10 oscillations. (a) If g = 9.80 m/s, what is the length of the pendulum? (b) When the mass is released from a certain hight, its speed as it passes through its lowest point is measured to be 1.850 m/s. Calculate the tension in the string at the pendulum's lowest point. (c) The 150.0 g mass is removed from the string forming the pendulum, and it is attached to a spring. If 27.00 seconds is required to complete 25 oscillations on the spring, calculate the spring constant. (d) If you are to move pendulum to another planet where g 6.78 m/s, how will period change? (e) Ifyou are to move spring mass system to another planet where g = 6.78 m/s, how will period change. (20 pts)

Explanation / Answer

a)

time period is T = 28/10 = 2.8 sec

g = 9.8 m/s^2

l = ?

T = 2*pi*sqrt(l/g)

2.8 = 2*3.142*sqrt(l/9.8)

l = 1.95 m

b) Tension in string is T

T -mg = m*v^2/R

T = mg + mv^2/R

T = (150*10^-3*9.8)+(150*10^-3*1.85^2/1.95)

T = 1.73 N

C) k = m*w^2

period is T = 27/25 = 1.08 sec

k= 150*10^-3*(2*3.142/1.08)^2

k = 5.1 N/m

d) period increases

Tnew = 2*3.142*sqrt(1.95/6.78) = 3.37 sec

e) period does not change

Tnew = 1.08 sec

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