Apendulum consists of a 1.5 kg stone swinging on a 4.3 m string of negligible mass. the stone has a speed of 8.4 m/s when it passes its lowest point. (a) what is the speed when the string is at 64 ˚ to the vertical? (b) what is the greatest angle with the vertical that the string will reach during the stone's motion? (c) if the potential energy of the pendulum-earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system?

(a) v = 1.54m/s, (b) Θ = 80.6° and (c) E = 52.92J

Explanation:

(a) At the lowest point, the total energy is giving by:

where,: kinetic energy,: potential energy, m: pendulum's mass, v: speed of the pendulum, g:gravity and y: heigh of the pendulum.

(1)  

When the string is at 64° from the vertical, the total energy is:    

(2)

At this point, is:

(3)

where L: longitude of the pendulum

By conservation of energy, we can calculate the speed of the string, at 64 ° to the vertical. Equaling equations (1) and (2):  

(b) Smilarly, by conservation of energy we can find the greatest angle, assuming that vf = 0 at the greatest angle reached:

Using the heigh calculated in equation (3) we can find the angle:

(c) The total mechanical energy at the lowest point is giving by:

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find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2