Mechano, the evil robot cat, has captured the mouse, Jerry (m_J = 0.400 kg), and
ID: 1451847 • Letter: M
Question
Mechano, the evil robot cat, has captured the mouse, Jerry (m_J = 0.400 kg), and is about to launch him out of a window using his robotic sling shot. You can see that the sling shot has two elastic bands that hold the pouch, which is wrapped around Jerry. Treat each of the bands like a Hooke's Law spring, with a spring constant of k = 1800 N/m. The rest length of each "spring" is L_0 = 0.0500 m. At the time of the launch, the "springs" have a length of L_f = 0.120 m. How much elastic potential energy (UE) is stored in each "spring?" What is Jerry's speed (v_J) when he leaves the sling shot?Explanation / Answer
The elastic potential energy stored in each spring is (1/2) k x2
Where k is the spring constant of each elastic band , x is the maximum displacement of the band
k = 1800 N /m , x = 0.120 m
U = (1/2) x 1800 x (0.120)2 = 13.0 J
B) When Jerry leaves the sling shot ,he will have the maximum velocity ,The maximum velocity is equal to the maximum potential energy he attained
The maximum potential energy of Jerry will be two times the maximum elastic energy of each band
i.e, 2 x 13 J = 26 J
(1/2) m v2 = 26 J
v = sqrt(2 x26 /0.450) = 10.7 m/s