EG260 Pre-course - -1 when at the highest point of the...

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@ Avril Slone 2008 1 of 2 EG-260 Dynamics 1 Pre-course Revision Questions 1. a. State what is meant by angular velocity. b. A stone is tied to one end of a cord and rotated in a horizontal circle about a point C with the cord horizontal, as shown in Figure 1. The stone has speed v and angular velocity w about C. The length of the cord is r. i. Write down the relationship between the speed v , the length of cord r and the angular velocity w. ii. Explain how v can be made to vary when w is constant. iii. Explain why there needs to be tension in the cord to maintain the circular motion. iv. Write down an expression for the acceleration of the stone in terms if v and r. Hence, if the stone has mass m , show that the tension in the cord, T is given by: w mv T = c. On one particular ride in an amusement park, passengers ‘loop-the loop’ in a vertical circle, seen in Figure 2 The loop has a radius of 7.0m and a passenger, mass 60 kg, is travelling at 12 ms
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Unformatted text preview: -1 when at the highest point of the loop. Assume that friction forces may be neglected and gravity, g = 9.81 N kg-1 C w v stone Figure 1 @ Avril Slone 2008 2 of 2 i. Calculate, for the passenger when at the highest point: a. The centripetal acceleration. b. The force the seat exerts on the passenger. ii. The passenger now moves and descends to the bottom of the loop. Calculate : a. The change in potential energy of the passenger in moving from the top to the bottom of the loop. b. The speed of the passenger on leaving the loop. iii. Operators of the ride must ensure the safety of the passengers and so must ensure that the speed at which the passengers enter the loop is above a certain minimum value. Suggest a reason for this. 2. Solve the second order differential equation 9 4 2 2 = + + t dt dx dt x d Figure 2 12 ms-1 7.0 m Passenger enters loop Passenger leaves loop...
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EG260 Pre-course - -1 when at the highest point of the...

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