The ball shown in the diagram is attached to a rotating pole with two strings. The ball has a mass of $0.250\mathrm{kg}$ and rotates in a horizontal circle at a speed of $8.0 \mathrm{m}/\mathrm{s}$.

Determine the tension in each string.

In an amusement park ride a cart of mass $300\mathrm{kg}$ and carrying four passengers each of mass $60\mathrm{kg}$ is dropped from a vertical height of $120\mathrm{m}$ along a frictionless path that leads into a loop-the-loop machine of radius $30\mathrm{m}$. The cart then enters a straight stretch from A to C, where friction brings it to rest after a distance of $40\mathrm{m}$.

a. Determine the velocity of the cart at A.

In an amusement park ride a cart of mass $300\mathrm{kg}$ and carrying four passengers each of mass $60\mathrm{kg}$ is dropped from a vertical height of $120\mathrm{m}$ along a frictionless path that leads into a loop-the-loop machine of radius $30\mathrm{m}$. The cart then enters a straight stretch from A to C, where friction brings it to rest after a distance of $40\mathrm{m}$.

b. Calculate the reaction force from the seat the cart onto the passenger at B.

In an amusement park ride a cart of mass $300\mathrm{kg}$ and carrying four passengers each of mass $60\mathrm{kg}$ is dropped from a vertical height of $120\mathrm{m}$ along a frictionless path that leads into a loop-the-loop machine of radius $30\mathrm{m}$. The cart then enters a straight stretch from A to C, where friction brings it to rest after a distance of $40\mathrm{m}$.

c. Determine the acceleration experienced by the cart from A to C.

A mass $\mathrm{m}$ is placed at the centre of a thin, hollow, spherical shell of mass $\mathrm{M}$ and radius $\mathrm{r}$ shown in the diagram $\mathrm{a}$. Determine the gravitational force the mass experiences.

A mass $\mathrm{m}$ is placed at the centre of a thin, hollow, spherical shell of mass $\mathrm{M}$ and radius $\mathrm{r}$ shown in the diagram $\mathrm{a}$. Determine the gravitational force the mass $\mathrm{m}$ exerts on $\mathrm{M}$