Question

Стальной шарик массой 10 г упал с высоты 1 м и подскочил после удара на высоту 0.8 м. Определите изменение импульса шарика.

Answer 1

Mgh1=(m/2)*(v1^2);
2*g*h1=v1^2
v1=sqrt(2gh1)
(m/2)*(v2^2)=m*g*h2
v2=sqrt(2gh2)
Импульс - это вектор.
Значение приращения импульса в проекции на вертикальную ось, направленную вверх равно:
p2-p1=m*v2-m*(-v1)=m*(v2+v1)=m*(sqrt(2gh2)+sqrt(2gh1)=0,01*(sqrt(2*9,8*1))=0,01*(3,96+4,43)= 0,0839 кг*(м/c)

Answer 2

Calculation of Change in Momentum

To determine the change in momentum of the steel ball, we need to calculate the initial momentum and the final momentum, and then find the difference between them.

The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the steel ball is 10 grams (0.01 kg) and the velocity can be calculated using the height from which it fell and the height it rebounded to.

Let's calculate the initial momentum first:

Initial momentum (p1) = mass (m) × initial velocity (v1)

The initial velocity can be calculated using the height from which the ball fell. Since the ball fell from a height of 1 meter, we can use the equation for gravitational potential energy to find the initial velocity:

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

Solving for velocity (v1):

v1 = √(2 × PE / m)

Substituting the given values:

v1 = √(2 × 0.01 kg × 9.8 m/s^2 × 1 m) = √(0.196) ≈ 0.443 m/s

Now we can calculate the initial momentum:

p1 = 0.01 kg × 0.443 m/s = 0.00443 kg·m/s

Next, let's calculate the final momentum:

Final momentum (p2) = mass (m) × final velocity (v2)

The final velocity can be calculated using the height to which the ball rebounded. Since the ball rebounded to a height of 0.8 meters, we can use the equation for gravitational potential energy to find the final velocity:

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

Solving for velocity (v2):

v2 = √(2 × PE / m)

Substituting the given values:

v2 = √(2 × 0.01 kg × 9.8 m/s^2 × 0.8 m) = √(0.1568) ≈ 0.396 m/s

Now we can calculate the final momentum:

p2 = 0.01 kg × 0.396 m/s = 0.00396 kg·m/s

Finally, we can find the change in momentum:

Change in momentum = final momentum (p2) - initial momentum (p1)

Change in momentum = 0.00396 kg·m/s - 0.00443 kg·m/s = -0.00047 kg·m/s

Therefore, the change in momentum of the steel ball is approximately -0.00047 kg·m/s.

Please note that the negative sign indicates a decrease in momentum, which is expected as the ball rebounded to a lower height.