Question

С наклонной плоскости высотой 3 м соскальзывает без трения тело массой 0,5кг. определить изменение импульса тела.

Answer 1

H=3 м    m=0.5 кг   Δp=?
===
Δp=m*Δv
vo=0
Δv=√(2*g*h)
Δp=m*√(2*g*h)=0.5*√(2*10*3)≈3.87 кг*м/с
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Answer 2

Calculation of Change in Momentum

To calculate the change in momentum of an object sliding down an inclined plane without friction, we need to consider the mass of the object and the change in velocity.

Given: - Mass of the object (m) = 0.5 kg - Height of the inclined plane (h) = 3 m

To find the change in momentum, we can use the formula:

Change in momentum (Δp) = Final momentum (p_f) - Initial momentum (p_i)

The momentum of an object can be calculated using the formula:

Momentum (p) = mass (m) × velocity (v)

Since the object is sliding down the inclined plane without friction, we can assume that the potential energy at the top of the incline is converted into kinetic energy at the bottom. Therefore, we can use the principle of conservation of energy to find the final velocity of the object.

The potential energy at the top of the incline is given by:

Potential energy (PE) = mass (m) × gravity (g) × height (h)

Using the given values, we can calculate the potential energy:

PE = 0.5 kg × 9.8 m/s² × 3 m = 14.7 J

Since the potential energy is converted into kinetic energy, we can equate the two:

Potential energy (PE) = Kinetic energy (KE)

KE = 0.5 × mass (m) × velocity² (v²)

Substituting the values, we get:

14.7 J = 0.5 × 0.5 kg × v²

Simplifying the equation, we find:

v² = (14.7 J) / (0.5 kg) = 29.4 m²/s²

Taking the square root of both sides, we find:

v ≈ √(29.4 m²/s²) ≈ 5.42 m/s

Now that we have the final velocity, we can calculate the final momentum:

Final momentum (p_f) = mass (m) × final velocity (v_f)

Substituting the values, we get:

p_f = 0.5 kg × 5.42 m/s = 2.71 kg·m/s

To find the initial momentum, we need to consider that the object starts from rest at the top of the incline. Therefore, the initial velocity (v_i) is 0 m/s.

Initial momentum (p_i) = mass (m) × initial velocity (v_i)

Substituting the values, we get:

p_i = 0.5 kg × 0 m/s = 0 kg·m/s

Now we can calculate the change in momentum:

Change in momentum (Δp) = Final momentum (p_f) - Initial momentum (p_i)

Substituting the values, we get:

Δp = 2.71 kg·m/s - 0 kg·m/s = 2.71 kg·m/s

Therefore, the change in momentum of the object sliding down the inclined plane without friction is approximately 2.71 kg·m/s.