K A Tsokos Solutions for Chapter: Mechanics, Exercise 3: Test yourself

A block of mass $2.0 \mathrm{kg}$ and an initial speed of $5.4 {\mathrm{ms}}^{-1}$ slides on a rough horizontal surface and is eventually brought to rest after travelling a distance of $4.0 \mathrm{m}$. Calculate the frictional force between the block and the surface.

A spring of spring constant $k=200 {\mathrm{Nm}}^{-1}$ is slowly extended from an extension of $3.0 \mathrm{cm}$ to an extension of $5.0 \mathrm{cm}$. Calculate the work done by the extending force.

The speed of the $8.0 \mathrm{kg}$ mass in position $\mathrm{A}$ in the diagram is $6.0 {\mathrm{ms}}^{-1}$. By the time it gets to $\mathrm{B}$ the speed is measured to be $12.0 {\mathrm{ms}}^{-1}$.

Estimate the frictional force opposing the motion. (The frictional force is acting along the plane.)

A mass $m$ of $4.0 \mathrm{kg}$ slides down a frictionless incline of $\theta ={30}^{°}$ to the horizontal. The mass starts from rest from a height of $20 \mathrm{m}$.

Sketch a graph of kinetic energy and potential energies of the mass as a function of distance travelled along the incline.

A mass $m$ of $4.0 \mathrm{kg}$ slides down a frictionless incline of $\theta ={30}^{°}$ to the horizontal. The mass starts from rest from a height of $20 \mathrm{m}$.

On each graph, sketch the sum of the potential and kinetic energies.

A battery toy car of mass $0.250 \mathrm{kg}$ is made to move up an inclined plane that makes an angle of $30°$ with the horizontal. The car starts from rest and its motor provides a constant acceleration of $4.0 {\mathrm{ms}}^{-2}$ for $5.0 \mathrm{s}$. The motor is then turned off

State the periods in the car's motion in which its mechanical energy is conserved.

A battery toy car of mass $0.250 \mathrm{kg}$ is made to move up an inclined plane that makes an angle of $30°$ with the horizontal. The car starts from rest and its motor provides a constant acceleration of $4.0 {\mathrm{ms}}^{-2}$ for $5.0 \mathrm{s}$. The motor is then turned off.

Estimate the average power developed by the car's motor.

A battery toy car of mass $0.250 \mathrm{kg}$ is made to move up an inclined plane that makes an angle of $30°$ with the horizontal. The car starts from rest and its motor provides a constant acceleration of $4.0 {\mathrm{ms}}^{-2}$ for $5.0 \mathrm{s}$. The motor is then turned off.

Determine the maximum power developed by the motor.