Ahorizontal block-spring system with the block on a frictionless surface has total mechanical energy e = 50.9 j and a maximum displacement from equilibrium of 0.204 m. (a) what is the spring constant? n/m (b) what is the kinetic energy of the system at the equilibrium point? j (c) if the maximum speed of the block is 3.45 m/s, what is its mass? kg (d) what is the speed of the block when its displacement is 0.160 m? m/s (e) find the kinetic energy of the block at x = 0.160 m. j (f) find the potential energy stored in the spring when x = 0.160 m. j (g) suppose the same system is released from rest at x = 0.204 m on a rough surface so that it loses 12.2 j by the time it reaches its first turning point (after passing equilibrium at x = 0). what is its position at that instant? m

(a) 2446 N/m

When the spring is at its maximum displacement, the elastic potential energy of the system is equal to the total mechanical energy:

where

U is the elastic potential energy

k is the spring constant

A is the maximum displacement (the amplitude)

Here we have

U = E = 50.9 J

A = 0.204 m

Substituting and solving the formula for k,

(b) 50.9 J

The total mechanical energy of the system at any time during the motion is given by:

E = K + U

where

K is the kinetic energy

U is the elastic potential energy

We know that the total mechanical energy is constant: E = 50.9 J

We also know that at the equilibrium point, the elastic potential energy is zero:

because x (the displacement) is zero

Therefore the kinetic energy at the equilibrium point is simply equal to the total mechanical energy:

(c) 8.55 kg

The maximum speed of the block is v = 3.45 m/s, and it occurs when the kinetic energy is maximum, so when

K = 50.9 J (at the equilibrium position)

Kinetic energy can be written as

where m is the mass

Solving the equation for m, we find the mass:

(d) 2.14 m/s

When the displacement is

x = 0.160 m

The elastic potential energy is

So the kinetic energy is

And so we can find the speed through the formula of the kinetic energy:

(e) 19.6 J

The elastic potential energy when the displacement is x = 0.160 m is given by

And since the total mechanical energy E is constant:

E = 50.9 J

the kinetic energy of the block at this point is

(f) 31.3 J

The elastic potential energy stored in the spring at any time is

where

k = 2446 N/m is the spring constant

x is the displacement

Substituting

x = 0.160 m

we find the elastic potential energy:

(g) x = 0

The postion at that instant is x = 0, since it is given that at that instant  the system passes the equilibrium position, which is zero.

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explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."

it was given as a lesson and guide for prayer.