Ish-energiya printsipi Konservativ bo'lmagan kuch Ishqalanish bilan qiyalik tekislikda harakat – Muammolar va yechimlar

2 Ish-energiya printsipi Konservativ bo'lmagan kuch Ishqalanish bilan qiyalik tekislikda harakat – Muammolar va yechimlar

1. Blok pastga sirg'alib tushadi qiyalik tekislik ishqalanish bilan. Blok nima? tezligi Blok yerga tushganda? koeffitsienti kinetik ishqalanish 0.4 ga teng. Tortishish kuchi tufayli tezlanish 10 m/s ga teng².

Ma'lum:

Boshlang'ich balandlik (h)_o) = 6 m

Yakuniy balandlik (h)_t) = 0 m

Boshlang'ich tezlik (v)_o) = 0 (dastlab dam olish holatida blok)

Kinetik ishqalanish koeffitsienti (μ_k) = 0.4

Gravitatsiya tufayli tezlanish (g) = 10 ms^-2

cos θ = adj/hyp = 8/10

The vertical component of vazn =w_y = w cos θ = m g cos θ = m (10)(8/10) = m (10)(4/5) = m (40/5) = 8 m

The normal kuch = N = w_y = 8 m

The force of kinetic friction = f_k = μ_k N = μ_k w_y = (0.4)(8 m) = 3.2 m

Qidirilgan: Yakuniy tezlik (v)_t)

yechim:

The work-mechanical energy principle states that the work done by the nonconservative forces acting on an object is equal to the total change in kinetic and potential energies.

W_nc = ΔEM

W_nc = ΔEK + ΔEP

W_nc = Work done by nonconservative force, ΔEM = The change in mexanik energiya, ΔEK = The change in kinetic energy, ΔEP = The change in potential energy.

O'zgarish kinetik energiya :

ΔEK = 1/2 m (v_t² - v_o²) = 1/2 m (v_t² – 0) = 1/2 mv_t²

O'zgarish potentsial energiya :

ΔEP = m g (h_t -h_o) = m (10)(0-6) = m (10)(-6) = – 60 m

Work done by the force of kinetic friction :

W_nc = – f_k s = – (3.2 m)(10) = – 32 m

Minus sign indicates that the work done by the force of kinetic friction on the block is negative.

Determine the final speed (v_t):

W_nc = ΔEK + ΔEP

– 32 m = 1/2 m v_t² - 60 m

– 32 m = m (1/2 v_t² - 60)

– 32 = 1/2 v_t² - 60

– 32 + 60 = 1/2 v_t²

28 = 1/2 v_t²

2 (28) = v_t²

56 = v_t²

v_t = √4.14

v_t = 2√14 m.s^-1

2.

A block slides down on an inclined plane with friction. The final speed of the block when it hits the ground is 10 m/s². If the friction force is 2 N and acceleration due to gravity is 10 m/s². What is the height of h?

Ma'lum:

Blokning massasi (m) = 1 kg

Boshlang'ich tezlik (v)_o) = 0 (dastlab dam olish holatida blok)

Yakuniy tezlik (v)_t) = 10 ms^-1

Boshlang'ich balandlik (h)_o) = h

Yakuniy balandlik (h)_t) = 0

Kinetik ishqalanish kuchi (f)_k) = 2 N

Gravitatsiya tufayli tezlanish (g) = 10 ms^-2

Qidirilgan: Balandligi (h)

yechim:

The work is done by the force of kinetic friction :

W_nc = – f_k d = – (2)(15) = – 30

Minus sign indicates that the work done by the force of kinetic friction on the block is negative.

Kinetik energiyaning o'zgarishi:

ΔEK = 1/2 m (v_t² - v_o²) = 1/2 (1)(10)² – 0) = 1/2 (10²) = 1/2 (100) = 50

Potensial energiyaning o'zgarishi:

ΔEP = m g (h_t -h_o) = (1)(10)(0-soat) = (10)(-soat) = -10 soat

The equation of the work-mechanical energy principle :

W_nc = ΔEK + ΔEP

– 30 = 50 – 10 soat

10 soat = 50 + 30

10 soat = 80

h = 80/10

h = 8 metr

1. What is the work-energy principle?
   • javob: The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, $W=\Delta KE$, qaerda $W$ is the work done and $\Delta KE$ is the change in kinetic energy.
2. How does a nonconservative force differ from a conservative force?
   • javob: A nonconservative force, like friction, results in a loss of mechanical energy from a system, typically in the form of heat. In contrast, conservative forces, like gravity or a spring force, don’t dissipate mechanical energy but rather can convert it between potential and kinetic energy within the system.
3. How does friction affect the work done on an object moving on an inclined plane?
   • javob: Friction acts in a direction opposite to the motion of the object. This means that friction does negative work on the object, reducing its kinetic energy or increasing the amount of external work required to move it up the incline.
4. Why doesn’t an object’s potential energy change due to nonconservative forces?
   • javob: Potential energy is associated with conservative forces, and its change depends on initial and final positions only, not on the path taken. Nonconservative forces can change the kinetic energy of an object but do not have associated potential energy.
5. How does the angle of inclination influence the motion of an object on an inclined plane with friction?
   • javob: The greater the angle of inclination, the larger the component of gravitational force acting parallel to the plane. This makes the object harder to keep at rest or move up the plane, and easier to accelerate down the plane. Friction acts to resist this motion, but its effect becomes relatively less significant as the angle increases.
6. Why do objects not accelerate indefinitely on an inclined plane with friction?
   • javob: Due to the presence of friction, as the object moves, some of the gravitational potential energy is transformed into heat. Eventually, the force due to gravity parallel to the plane will be balanced out by the frictional force, and the object will move with a constant velocity or come to rest.
7. Can the work done by a nonconservative force be recovered?
   • javob: The work done by nonconservative forces usually gets transformed into forms of energy like heat, which are generally more challenging to convert back into useful mechanical energy. In most practical scenarios, this energy is considered “lost” to the system.
8. What determines the magnitude of the frictional force on an inclined plane?
   • javob: The frictional force on an inclined plane is determined by the normal (perpendicular) force and the coefficient of friction between the surfaces. It’s given by ffrictionمور=μ×fnormalمور, qaerda $\mu$ is the coefficient of friction.
9. Why is potential energy defined as zero at some reference point?
   • javob: Potential energy is a relative measure. By defining a reference point where potential energy is zero, it provides a consistent basis for calculating changes in potential energy for various positions relative to that reference.
10. How would the motion of an object on an inclined plane change if there were no friction?

• javob: Without friction, the only force acting on the object along the plane would be the component of gravity parallel to the incline. As a result, the object would accelerate down the plane solely due to this force and not reach a constant velocity unless acted upon by some other external force.