state and prove work energy theorem
Answers
Answered by
2
The Work-Energy Theorem
The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
image
Kinetic Energy: A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the work-energy theorem.
The work W done by the net force on a particle equals the change in the particle’s kinetic energy KE:
W
=
Δ
KE
=
1
2
mv
2
f
−
1
2
mv
2
i
W=ΔKE=12mvf2−12mvi2
where vi and vf are the speeds of the particle before and after the application of force, and m is the particle’s mass.
Derivation
For the sake of simplicity, we will consider the case in which the resultant force F is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration a along a straight line. The relationship between the net force and the acceleration is given by the equation F = ma (Newton’s second law), and the particle’s displacement d, can be determined from the equation:
v
2
f
=
v
2
i
+
2
ad
vf2=vi2+2ad
obtaining,
d
=
v
2
f
−
v
2
i
2
a
d=vf2−vi22a
The work of the net force is calculated as the product of its magnitude (F=ma) and the particle’s displacement. Substituting the above equations yields:
W=Fd=mav2f−v2i2a=12mv2f−12mv2i=K−KEi=ΔKE
The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
image
Kinetic Energy: A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the work-energy theorem.
The work W done by the net force on a particle equals the change in the particle’s kinetic energy KE:
W
=
Δ
KE
=
1
2
mv
2
f
−
1
2
mv
2
i
W=ΔKE=12mvf2−12mvi2
where vi and vf are the speeds of the particle before and after the application of force, and m is the particle’s mass.
Derivation
For the sake of simplicity, we will consider the case in which the resultant force F is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration a along a straight line. The relationship between the net force and the acceleration is given by the equation F = ma (Newton’s second law), and the particle’s displacement d, can be determined from the equation:
v
2
f
=
v
2
i
+
2
ad
vf2=vi2+2ad
obtaining,
d
=
v
2
f
−
v
2
i
2
a
d=vf2−vi22a
The work of the net force is calculated as the product of its magnitude (F=ma) and the particle’s displacement. Substituting the above equations yields:
W=Fd=mav2f−v2i2a=12mv2f−12mv2i=K−KEi=ΔKE
Answered by
2
Answer:
Explanation:
According to this theorm the change in kinetic energy of an object is equal to the work done by the object
⚽➡️U ----------------→ ⚽➡️V
after time (T)
|←---------Distance (d)---→|
V² = U² + 2as ( s =Distance)
V² = U² + 2ad ---( eq 1 )
Multiply eq (1) with 'm' on both side
mv² = mu² + 2 m*ad
mv² - mu² = 2m*ad
mv² - mu² = 2 F*d ( m*a = force )
½mv² +½ mu² = F*d
Kinetic energy final - Kinetic energy initial = Work (W)
W =∆K energy
Similar questions