Question

In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg. m2/s) at the lowest point of its path relative to the center of the circle is approximately Select one: a. 40 b. 10 C. 30 O d. 20 e. 50

Answer 1

The angular momentum of the weight at the lowest point can be found by using the principle of conservation of energy to calculate the velocity at that point and then using the formula L = m * r * v, considering the mass of the weight and the length of the string as the radius.

Step-by-step explanation:

The problem is asking to determine the angular momentum of a 1.6-kg weight at the lowest point of its path after being released from a horizontal position with zero initial velocity. The weight swings at the end of a 2-meter long string. To find the angular momentum, we first need to calculate the velocity of the weight at the bottom of the swing.

Since there is initial release from rest, potential energy at the top is converted entirely into kinetic energy at the bottom of the swing. We can set up the conservation of energy as follows:

Potential energy at the top (PEtop) = m * g * h

Kinetic energy at the bottom (KEbottom) = (1/2) * m * v2

The height (h) from which the weight is released is equal to the length of the string when the weight is at rest in the horizontal position, so h = 2 m. The mass (m) of the weight is 1.6 kg, and standard gravitational acceleration (g) is 9.8 m/s2. We can solve for velocity (v) at the bottom of the swing using the equation:

PEtop = KEbottom
m * g * h = (1/2) * m * v2
1.6 kg * 9.8 m/s2 * 2 m = (1/2) * 1.6 kg * v2

From this, we find that velocity v = sqrt(2 * g * h).

Finally, angular momentum (L) at the lowest point is given by:

L = m * r * v

Where r is the radius of the circle (length of string = 2 m). Using the velocity found earlier, we can calculate the exact value and then match it to one of the given choices.

Answer 2

To find the angular momentum of the weight at the lowest point of its path, we can use the conservation of angular momentum. The angular momentum of the weight is equal to the product of its moment of inertia and its angular velocity.

Step-by-step explanation:

To find the angular momentum of the weight at the lowest point of its path, we can use the conservation of angular momentum. The angular momentum of the weight is equal to the product of its moment of inertia and its angular velocity. The moment of inertia of a point mass rotating in a circle can be calculated using the formula I = m * r^2, where m is the mass and r is the radius. In this case, the weight is rotating in a circle with a radius of 2 m, so its moment of inertia is I = (1.6 kg) * (2 m)^2 = 6.4 kg.m^2.

Therefore, the angular momentum of the weight at the lowest point of its path is equal to the product of the moment of inertia and the angular velocity, which is (6.4 kg.m^2) * (6.26 rad/s) = 40.064 kg.m^2/s. Rounded to one decimal place, the angular momentum is approximately 40 kg.m^2/s.