In its general form, the conservation of energy involves mechanical energy (kine

Question

In its general form, the conservation of energy involves mechanical energy (kinetic + potential), and thermal energy. When we deal with sliding objects, and there is kinetic friction, the force of friction itself does Work on the moving object.

b. Compute the kinetic energy at x1 and x2. Verify that the Work-energy theorem is valid.

This exercise is an example of conservation of total energy (mechanical + thermal), which can be stated as:

EK + Wfriction = constant

where Wfriction is the amount of heat dissipated through friction. Sometimes Wfriction is also denoted by Q.

Explanation / Answer

Given,

Coefficient of Friction = k = 0.4

Mass = 10kg

Friction Force = k * N = k * m * g

Friction Force = 39.2N

We know ,

Force = m * a

Only force active on Mass, from point X1 = Friction force.

Friction Force = m * a

k * m * g = m * a

Acceleration (a) = k * g = 3.92m/s^2 (direction opposing motion)

Now ,

Velocity at x2 (V2) = 0

Valocity at x1 (V1) = 2m/s

V2^2 = V1^2 + 2* a * s

Where s is distance travelled

0 = 4 -2 * 3.92 * s

s = 0.51 m

Distance travelled = 0.51m

Work done = F * S

Work done by force of friction = 39.2 * 0.51 J

Work done by force of friction = 20J

b)

Kinetic energy = 0.5 * m * V^2

AT X1 -

K.E = 0.5 * 10 * 2^2

Kinetic energy at X1 = 20J

AT X2 -

Kinetic energy at X2 = O , Because velocity is Zero.

Change in Kinetic Energy = Kinetic energy at X1 - Kinetic energy at X2

Change in Kinetic Energy = 20J

According to Work energy theorem , Change in Kinetic Energy = Work done = 20J Hence Verified.

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