To solve this problem, we need to use the principle of conservation of energy. The pendulum starts with potential energy and no kinetic energy at the top of its swing, and it has maximum kinetic energy and no potential energy at the bottom of its swing.

1. First, we calculate the height (h) at which the pendulum bob is initially held. This can be found using the equation h = L - Lcosθ, where L is the length of the pendulum and θ is the angle. Substituting the given values, we get h = 2.00 m - 2.00 m cos(30.0°) = 0.133974596 m.

2. Next, we calculate the initial potential energy (PE) of the pendulum bob using the equation PE = mgh, where m is the mass of the bob, g is the acceleration due to gravity, and h is the height we just calculated. Substituting the given values, we get PE = 0.1 kg * 9.8 m/s² * 0.133974596 m = 0.131334584 J.

3. Since the pendulum bob has no kinetic energy at the top of its swing, all of its energy is potential energy. Therefore, at the bottom of its swing, all of this energy will have been converted into kinetic energy (KE).

4. We can find the maximum speed of the pendulum bob by setting its kinetic energy equal to the initial potential energy and solving for velocity. The equation for kinetic energy is KE = 1/2 mv². Setting this equal to the initial potential energy, we get 0.131334584 J = 1/2 * 0.1 kg * v².

5. Solving this equation for v, we get v = sqrt((2 * 0.131334584 J) / 0.1 kg) = 1.62 m/s.

So, the maximum speed of the mass is 1.62 m/s. Therefore, the answer is a. 1.62 m/s.

Question

To solve this problem, we need to use the principle of conservation of energy. The pendulum starts with potential energy and no kinetic energy at the top of its swing, and it has maximum kinetic energy and no potential energy at the bottom of its swing.

1. First, we calculate the height (h) at which the pendulum bob is initially held. This can be found using the equation h = L - Lcosθ, where L is the length of the pendulum and θ is the angle. Substituting the given values, we get h = 2.00 m - 2.00 m cos(30.0°) = 0.133974596 m.

2. Next, we calculate the initial potential energy (PE) of the pendulum bob using the equation PE = mgh, where m is the mass of the bob, g is the acceleration due to gravity, and h is the height we just calculated. Substituting the given values, we get PE = 0.1 kg * 9.8 m/s² * 0.133974596 m = 0.131334584 J.

3. Since the pendulum bob has no kinetic energy at the top of its swing, all of its energy is potential energy. Therefore, at the bottom of its swing, all of this energy will have been converted into kinetic energy (KE).

4. We can find the maximum speed of the pendulum bob by setting its kinetic energy equal to the initial potential energy and solving for velocity. The equation for kinetic energy is KE = 1/2 mv². Setting this equal to the initial potential energy, we get 0.131334584 J = 1/2 * 0.1 kg * v².

5. Solving this equation for v, we get v = sqrt((2 * 0.131334584 J) / 0.1 kg) = 1.62 m/s.

So, the maximum speed of the mass is 1.62 m/s. Therefore, the answer is a. 1.62 m/s.

Knowee AI · Accepted Answer

To solve this problem, we need to use the principle of conservation of energy. The pendulum starts with potential energy and no kinetic energy at the top of its swing, and it has maximum kinetic energy and no potential energy at the bottom of its swing.

1. First, we calculate the height (h) at which the pendulum bob is initially held. This can be found using the equation h = L - Lcosθ, where L is the length of the pendulum and θ is the angle. Substituting the given values, we get h = 2.00 m - 2.00 m cos(30.0°) = 0.133974596 m.

2. Next, we calculate the initial potential energy (PE) of the pendulum bob using the equation PE = mgh, where m is the mass of the bob, g is the acceleration due to gravity, and h is the height we just calculated. Substituting the given values, we get PE = 0.1 kg * 9.8 m/s² * 0.133974596 m = 0.131334584 J.

3. Since the pendulum bob has no kinetic energy at the top of its swing, all of its energy is potential energy. Therefore, at the bottom of its swing, all of this energy will have been converted into kinetic energy (KE).

4. We can find the maximum speed of the pendulum bob by setting its kinetic energy equal to the initial potential energy and solving for velocity. The equation for kinetic energy is KE = 1/2 mv². Setting this equal to the initial potential energy, we get 0.131334584 J = 1/2 * 0.1 kg * v².

5. Solving this equation for v, we get v = sqrt((2 * 0.131334584 J) / 0.1 kg) = 1.62 m/s.

So, the maximum speed of the mass is 1.62 m/s. Therefore, the answer is a. 1.62 m/s.

A simple pendulum of length 2.00 m has a mass of 100 g attached. It is drawn back 30.0° and then released. What is the maximum speed of the mass?Select one:a.1.62 m/sb.4.58 m/sc.1.14 m/sd.2.29 m/s

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