Answer:
3MN/m
Explanation:
Step one:
given data
Kinetic Energy KE=15,000J
mass m= 0.5kg
compression x= 0.1m
Step two:
The expression for the energy stored in spring is
[tex]KE= 1/2ke^2\\\\15000=1/2 *k*0.1^2\\\\15000=1/2*k*0.01\\\\15000=0.005k\\\\[/tex]
divide both sides by
0.005
[tex]k= 15000/0.005\\\\k=3000000\\\\k= 3MN/m[/tex]
From conservation of energy, the value of the spring constant for the tennis ball launcher according to the data is 3 x [tex]10^{6}[/tex] Nm
The work done by a tennis ball launcher by using a spring to propel the ball forward is equal to the kinetic energy which is 15,000 Joule. That is,
W = K.E
The given parameters are:
K.E = 15,000 J
Mass m = 0.5 kg
compression x = 0.1 m
The elastic potential energy on the spring will be equal to the work done by the tennis ball launcher. That is,
E = W
since W = K.E
E = K.E
1/2k[tex]x^{2}[/tex] = 1/2m[tex]v^{2}[/tex] = 15,000
1/2k[tex]x^{2}[/tex] = 15000
Substitute for 0.1 for x
1/2 K ([tex]0.1^{2}[/tex]) = 15000
[tex]0.1^{2}[/tex] K = 30000
K = 30000/0.01
K = 3 x [tex]10^{6}[/tex] Nm
Therefore, the value of the spring constant for the tennis ball launcher according to the data is 3 x [tex]10^{6}[/tex] Nm
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