Chapter 4

Consider a ${10}^4\mathrm{kg}$ spaceship in deep space. Suppose the spaceship's thruster produces $100\mathrm{N}$ of constant thrust. If the spaceship is moving at $50\mathrm{m}/\mathrm{s}$ and the thruster is anti- aligned with the spaceship's velocity, how long should the thruster fire to bring the spaceship to rest with respect to absolute space?

A hockey player hits a puck of mass $m_P$ into a semicircular groove in the ice of radius $R$. The ice has coefficient of Coulomb friction ${\mu }_c$. What is the impulse that must be imparted to the puck at the entrance to the groove such that it makes it around the semicircle exactly once before stopping?

A particle slides freely on a flat surface, attached to a massless string that passes through a hole in the surface. At a given moment, the particle is moving in a circle of radius $r_0$ with angular velocity ${\omega }_0$. Assume that the string is pulled through the hole at a constant rate. Find an expression for the tension in the string as a function of the length $r$ of string left on the surface.

A particle slides freely on a flat surface, attached to a massless string that passes through a hole in the surface. At a given moment, the particle is moving in a circle of radius $r_0$ with angular velocity ${\omega }_0$. Assume that the string is pulled through the hole at a constant rate. Find an expression for the tension in the string as a function of the length $r$ of string left on the surface.