You use a slingshot to launch a 40 g stone upward at an angle (not straight upwa

Question

You use a slingshot to launch a 40 g stone upward at an angle (not straight upward). The spring has a spring constant of 100 N/m and an unstretched length of 10 cm. To launch the stone you stretch the elastic to 30 cm. At the highest point in its flight, the stone moves at 5 m/s. Ignore friction and air resistance, and assume the initial height of 1.7 m. Full points will be awarded for the correct answer to the following question: What is the height of the highest point in the flight? ___ If the full credit cannot be awarded, then partial credit will be awarded for the correct answers to the following questions: i) What is the initial stretch of the elastic? ___ ii) What is the initial potential energy of the stretched elastic? ___ iii) What is the initial kinetic energy of the stone before elastic is released? ___ iv) What is the gravitational energy of the stone before the elastic is released? ___ v) What is the total energy of the system just before the elastic is released? ___ vi) What is the total energy of the system once the stone is at the highest point? ___ vii) Why is the kinetic energy of the stone at the highest point of trajectory is NOT zero? ___ viii) What is the kinetic energy of the stone at the highest point? ___ ix) What is the potential energy of the dart when it is at the highest point? ___ x) What is the height of the dart at the highest point? ___

Explanation / Answer

(1) elongation of elatic= 30-10= 20cm=0.2 m

mass= 40g=0.04kg

initial velocity=0

using the conservation of energy

1/2kx2=mgh + 1/2 mv2 .

(1/2)(100)(0.2)2= 0.04(9.8)(h)+ 1/2 *0.04*52 .

h= 3.83 m.

(i)x= 30-10= 20 cm

(ii)Pe= 1/2 kx2=(1/2)(100)(0.2)2= 2 j

(iii)initial KE= 0

(iv)initial gravitational PE=0

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