A bob is suspended from a crane by a cable of length l=5 m. The crane and the bob are moving at

step 1 In this question we have given that a bob is suspended from a crane by a cable of length 5 meter

A bob is suspended from a crane by a cable of length l=5 m....

A bob is suspended from a crane by a cable of length $l=5 \mathrm{~m}$. The crane and the bob are moving at a constant speed $v_{0} .$ The crane is stopped by a bumper and the bob on the cable swings out an angle of $60^{\circ} .$ The initial speed $v_{0}$ is $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) $10 \mathrm{~m} / \mathrm{s}$ (B) $7 \mathrm{~m} / \mathrm{s}$ (C) $4 \mathrm{~m} / \mathrm{s}$ (D) $2 \mathrm{~m} / \mathrm{s}$

A bob is suspended from a crane by a cable of length $l=5 \mathrm{~m}$. The crane and the bob are moving at a constant speed $v_{0} .$ The crane is stopped by a bumper and the bob on the cable swings out an angle of $60^{\circ} .$ The initial speed $v_{0}$ is $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $10 \mathrm{~m} / \mathrm{s}$
(B) $7 \mathrm{~m} / \mathrm{s}$
(C) $4 \mathrm{~m} / \mathrm{s}$
(D) $2 \mathrm{~m} / \mathrm{s}$

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object has due to its motion and is proportional to the square of its speed. Initially, when the bob is in motion, the kinetic energy is at a maximum, and as it swings upward, this energy is gradually transformed into gravitational potential energy, slowing the bob down until it momentarily comes to rest.

Pendulum Geometry

The pendulum geometry is important for determining the change in vertical height as the bob swings to a given angle from the vertical. By understanding the relationship between the length of the pendulum and the cosine of the swing angle, one can calculate the vertical displacement, which is essential for applying energy conservation principles to determine unknown variables such as initial speed.

Conservation of Mechanical Energy

This principle states that in an isolated system with no non-conservative work (like friction) done on it, the total energy remains constant. In dynamics problems such as a swinging bob, the initial kinetic energy is converted into gravitational potential energy as the bob rises to its highest point, allowing us to relate velocity and height change.

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. As the bob swings upward, its vertical height increases, leading to an increase in gravitational potential energy. This change is calculated by the product of mass, gravitational acceleration, and the change in height.

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