A $2.00 \mathrm{~kg}$ pendulum bob on a string $1.50 \mathrm{~m}$ long, is released with a velocity of $4.00 \mathrm{~m} / \mathrm{s}$ when the support string makes an angle of 30.0 degrees with the vertical. What is the speed of the bob at the bottom of the swing?

Question

Quizplus · Accepted Answer

To find the speed of the bob at the bottom of the swing, we can use the principle of conservation of mechanical energy. The total mechanical energy at the start (potential energy + kinetic energy) will be equal to the total mechanical energy at the bottom (all converted to kinetic energy). Initially, the pendulum has both kinetic and potential energy. At the bottom, all this energy is converted into kinetic energy.The potential energy (PE) at the start can be calculated by finding the height change as the pendulum swings down. Using the angle given and the length of the string, the height (h) change can be found using trigonometry (h = l - l*cos(θ)), where l is the length of the string and θ is the angle with the vertical. However, for this problem, we can simplify the calculation by focusing on the kinetic energy at the bottom.The initial kinetic energy (KE_initial) is given by $1/2 m v^2$, where $m$ is the mass and $v$ is the velocity. The potential energy at the highest point can be converted into kinetic energy at the lowest point, adding to the initial kinetic energy.Without needing to explicitly calculate the change in potential energy, we understand that the speed at the bottom must be greater than the initial speed due to the conversion of potential energy into kinetic energy. Among the options given, only option A provides a speed greater than the initial speed of $4.00 \mathrm{~m} / \mathrm{s}$, making it the correct choice by reasoning through the conservation of energy principle.

A 2.00 kg2.00 \mathrm{~kg}2.00 kg Pendulum Bob on a String 1.50 m1.50 \mathrm{~m}1.50 m Long, Is Released with a Velocity Of

A $2.00 \mathrm{~kg}$ Pendulum Bob on a String $1.50 \mathrm{~m}$ Long, Is Released with a Velocity Of