9 Conservation of energy and Heat In its general form, the conservation of energ
ID: 1403073 • Letter: 9
Question
9 Conservation of energy and Heat In its general form, the conservation of energy involves mechanical energy (kit kinetic friction, the force of friction itself does Work on the moving object. 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 a. Take an object of mass m = 10 kg sliding on a surface where the coefficient of kinetic friction is k 0.4. Suppose that initially the block is moving at constant speed vi 2 m/s (an external force is balancing the friction). Then, constant speed vi- 2 m/s (an external force is balancing the friction). Then at position ri, the external force disappears. Compute the acceleration of the object, and the length travelled before it comes to a complete stop at position T2. Then, calculate the work done by the force of friction between zi and z2. This work is the amount of energy that has been dissipated as heat. b. Compute the kinetic energy at ri and at r. Verify that the Work-energy This exercise is an example of conservation of total energy (mechanical + thermal) Where W friction is the amount of heat dissipated through friction. Sometimes Wriation theorem is valid. which can be stated as: EK + Wfriction const. is also denoted by Q
Explanation / Answer
at point x1 the frictional force balacne with the applied force so,
Friction Force = m a
U_k m g = m a
a = U_k g = 0.4 ( 9.8) = 3.92m/s^2
Velocity at x2 is V2 = 0
Valocity at x1 is V1= 2m/s
from the kinematic equation
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
the expression for work is
W = F S
= 39.2 (0.51 J) = 20 J
b)
the kinetic energy at X1 is
KE= 0.5 * m * V1^2
K.E = 0.5 (10 )2^2 = 20 J
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
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