A steel ball of mass 0.500 kg is fastened to a cord that is 70.0 cm long and fixed at the far en

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A steel ball of mass 0.500 kg is fastened to a cord that is...

A steel ball of mass 0.500 $\mathrm{kg}$ is fastened to a cord that is 70.0 $\mathrm{cm}$ long and fixed at the far end. The ball is then released when the cord is horizontal (Fig. $9-65$ ). At the bottom of its path, the ball strikes a 2.50 $\mathrm{kg}$ steel block initially at rest on a frictionless surface. The collision is elastic. Find (a) the speed of the ball and (b) the speed of the block, both just after the collision.

A steel ball of mass 0.500 $\mathrm{kg}$ is fastened to a cord that is 70.0 $\mathrm{cm}$ long
and fixed at the far end. The ball is then
released when the cord is horizontal (Fig. $9-65$ ). At the bottom of its path,
the ball strikes a 2.50 $\mathrm{kg}$ steel block initially at rest on a frictionless surface.
The collision is elastic. Find (a) the speed of the ball and (b) the speed of
the block, both just after the collision.

Key Concepts

Gravitational Potential Energy

This is the energy an object possesses due to its position in a gravitational field. In problems where an object is raised to a height, the energy stored as gravitational potential energy can be converted into kinetic energy when the object is allowed to fall, which is key to determining its speed just before impacting another object.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed but only transformed from one form to another. In mechanics, this is used to relate the loss of gravitational potential energy to the gain in kinetic energy, enabling the calculation of velocity when an object is released from a height.

Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. This concept is essential when analyzing interactions between objects, as it allows for the determination of post-collision velocities using the conservation laws, provided that no energy is lost to deformation, sound, or heat.

Conservation of Momentum

The principle of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant. This concept is used in collision problems to relate the velocities and masses of colliding bodies before and after impact, making it a fundamental tool for solving dynamics problems involving two or more objects.

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