Question

Mechano, the evil robot cat, has captured the mous

Mechano, the evil robot cat, has captured the mouse, Jerry (mJ = 0.500 kg), and is about to launch him out of a window using his robotic sling shot.

Part A: 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 L0 = 0.0550 m. At the time of the launch, the \"springs\" have a length of Lf = 0.100 m.

Part B: What is Jerry\'s speed (vJ) when he leaves the sling shot?

Answer 1

a) potential energy in the spring = 1.8225 J

b) Jerry's speed = 2.744 m/s

Step-by-step explanation:

a) The spring constant, k = 1800 N/m

The rest length of the spring,
`L_(0) = 0.0550 m`

The launch length,
`L_(f) = 0.100 m`

The potential energy of each spring is ,
`PE = 0.5 k(\triangle x)^(2)`

`\triangle x = 0.1 - 0.055 = 0.045 m`

`PE = 0.5 * 1800* 0.045^(2)`

PE = 1.8225 J

b) To get Jerry's speed, use the law of energy conservation

PE energy in the string = KE of the robot

`KE = 0.5mv^(2)`

PE in the spring = 1.8225 J

`1.8825 = 0.5 mv^(2) \\1.8825 = 0.5 * 0.5 v^(2) \\1.8825 = 0.25 v^(2) \\ v^(2) = 1.8825/0.25\\v^(2) = 7.53`

v = 2.744 m/s