A2.0-kg mass is attached to one end of a spring with a spring constant of 100 n/m and a 4.0-kg mass is attached to the other end. the masses are placed on a horizontal frictionless surface and the spring is compressed 10 cm. the spring is then released with the masses at rest and the masses oscillate. when the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s. the mechanical energy that has been lost to this instant is:

mechanical energy that has been lost to this instant is 0.3056 J

Explanation:

given data

mass m1 = 2 kg

spring constant k =  100 N/m

mass m2 = 4 kg

spring compressed x = 10 cm

speed = 0.36 m/s

solution

we know that initial energy is

initial energy= 0.5 k x²

initial energy  = 0.5 × 100 × 0.1²

initial energy  = 0.5 J

and

momentum  conservation is

2 × 0.36 = 4 v

so v = 0.18 m/s

and

energy lost will be here

energy lost = 0.5 - (0.5 × 2 × 0.36² + 0.5 × 4 × 0.18²)

energy lost =  0.3056 J

so mechanical energy that has been lost to this instant is 0.3056 J

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.

490 n

f=125n a=2.5m/s2