Movimiento de rodadura: problemas y soluciones

1. Un objeto cilíndrico hueco (I = m R² ⁾ rueda sin deslizarse por un plano inclinado rugoso con una velocidad inicial de 10 m/s. El plano inclinado tiene un ángulo de elevación θ con tan θ = 0.75. Si la aceleración gravitatoria g = 10 m/ ^s² , la velocidad del objeto se reduce a 5 m/ ^s, entonces la distancia recorrida por el objeto en el plano inclinado es…

Conocido :

Momento de inercia del cilindro hueco (I) = m R ²

Ángulo de elevación = θ , donde tan θ = 0.75 = 75/100 = opp / adj

Sin θ = opp / hyp = 75/125 = 3/5 = 0.6

Aceleración debida a la gravedad (g) = 10 m/ ^s²

Velocidad inicial (v _o ) = 10 m/s

Velocidad final (v _t ) = 5 m/s

Buscado : Distancia

solución:

Calculate the height reached by the cylinder using equation of the conservación de la energía mecánica.

Initial height (h_o) = 0 metro

Velocidad inicial (v_o) = 10 m/s

Velocidad final (v_t) = 5 m/s

Aceleración debida a la gravedad (g) = 10 m/s²

The cylinder reaches a height of 7.5 meters.

Distance traveled by cylinder :

The distance traveled by the cylinder is 12.5 metros.

La respuesta correcta es la A.

Description of the equation :

_o = initial, _t = final, ME = energía mecánicaEN = potential energy, KE = energía cinética, m = masa, g = acceleration due to gravity, h = height, v = linear velocity, ω = velocidad angular, I = moment of inertia, R = radius of cylinder

2. A solid cylinder (I = ½ m R²) with a mass of 3 kg moves to roll without slipping up a rough inclined plane having an elevation angle θ with sin θ = 0.6. If the gravitational acceleration g = 10 m.s^-2 and the initial velocity of the object is 10 m/s, then the length of the inclined plane traveled by an object is…

Conocido :

Moment of inertia of solid cylinder (I) = ½ m R²

Mass of cylinder = 3 kg

Velocidad inicial (v _o ) = 10 m/s

Velocidad final (v_t) = 0 m/s (object stop)

Elevation angle (θ) = θ, where sin θ = 0.6 = 6/10 = opp/hyp

Aceleración debida a la gravedad (g) = 10 m/s²

Buscado : The length of the inclined plane traveled by object

solución:

Calculate the height reached by the cylinder using equation of the conservation of mechanical energy.

Initial height (h_o) = 0 metro

Velocidad inicial (v_o) = 10 m/s

Velocidad final (v_t) = 0 m/s (object stop)

Aceleración debida a la gravedad (g) = 10 m/s²

The cylinder reaches a height of 7.5 meters.

Distance traveled by cylinder :

The distance traveled by the cylinder is 12.5 meters.

3. Un objeto cilíndrico hueco (I = m R²) with radius R, moves to roll without slipping up a rough inclined plane with an angle of α where sin α = 0.8. If the gravitational acceleration g = 10 m.s^-2 and the initial velocity is 8 m.s^-1 then the length of the inclined plane reached by the object before it stops is…

Conocido :

Moment of inertia of solid cylinder (I) = m R²

Velocidad inicial (v _o ) = 8 m/s

Velocidad final (v_t) = 0 m/s (object stop)

Elevation angle of inclined plane (θ) = θ, where sin θ = 0.8

Aceleración debida a la gravedad (g) = 10 m/ ^s²

Buscado : Distance traveled by cylinder

solución:

Calculate the height reached by the cylinder using equation of the conservation of mechanical energy.

Initial height (h_o) = 0 metro

Velocidad inicial (v_o) = 8 m/s

Velocidad final (v_t) = 0 m/s

Aceleración debida a la gravedad (g) = 10 m/s²

The cylinder reaches a height of 6.4 meters.

Distance traveled by cylinder :

The distance traveled by the cylinder is 8 meters.