AC Kuwait Assessment Tool and Marking Guide Task/Exercise 2: (6 marks) A ball of

Question

AC Kuwait Assessment Tool and Marking Guide Task/Exercise 2: (6 marks) A ball of mass m-2.1 kg is released from rest at a height of h 75 cm above a vertical spring of force constan k' as shown in the figure below. The ball strikes the top of the spring and compresses it a distance d-0.00 Neglecting any energy losses during the collision; a. What is the speed of the ball just as it touches the spring? (3 marks) b. Calculate the force constant of the spring. (1.5 marks) c. Find the power if the time of the strike is 0.1 min. (1.5 marks) CASIO -8SES PL

Explanation / Answer

a) Using the kinematic equation .. v² = u² + 2gh .. (initial vel u = 0)

v = sqrt(2 x 9.80 x 0.75m)

v= 3.834 m/s

b) At max compression (d=0.09m) the total GPE lost = Elastic PE gained (KE = 0)

mgH = ½ke² .. (H = 0.75+0.09 = 0.84m)
k = 2mgH / e²
k = (2 x 2.10kg x 9.80 x 0.84m) / (0.09m)²

k =4268.44 N/m

(C)

Power = ( change in energy/ time taken)

= (0.5ke^2/0.1*60)

= (0.5*4268.44*0.09^2/6)

= 2.88 W

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