Chapter 1: Mechanics

A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes

(a) parallel to the incline and

(b) parallel to the floor.

When a body of unknown mass is attached to an ideal spring with force constant 120 N/m, it is found to vibrate with a frequency of 6.00 Hz. Find (a) the period of the motion; (b) the angular frequency; (c) the mass of the body.

Scientists have found evidence that Mars may once have had an ocean 0.500 km deep. The acceleration due to gravity on Mars is 3.71 m/s². (a) What would be the gauge pressure at the bottom of such an ocean, assuming it was freshwater? (b) To what depth would you need to go in the earth’s ocean to experience the same gauge pressure?

A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is constant and equal to$\mathbf{0}\mathbf{.}\mathbf{200}\mathbf{}\mathit{r}\mathit{a}\mathit{d}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$, what is its angular velocity at t = 2.50 s ? (b) Through what angle has the wheel turned between t = 0 and $\mathit{t}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{50}\mathit{s}$ ?

The flywheel of an engine has a moment of inertia 1.60 kg m² about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8.00 s, starting from the rest?

A 0.160-kg hockey puck is moving on an icy, frictionless,

horizontal surface. At $\mathit{t}\mathbf{=}\mathbf{0}$, the puck is moving to the right at $\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$.

(a) Calculate the velocity of the puck (magnitude and direction) after a force of 25.0 N directed to the right has been applied for 0.050 s. (b) If, instead, a force of 12.0 N directed to the left is applied from t= 0 to t= 0.050 s, what is the final velocity of the puck?

A $\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{-}\mathit{N}$350-N, uniform, $\mathbf{60}\mathbf{.}\mathbf{0}\mathbf{-}\mathit{m}$1.50-m bar is suspended horizontally by two vertical cables at each end. Cable A can support a maximum tension of 500.0 N without breaking, and cable B can support up to$\mathbf{25}\mathbf{.}\mathbf{0}\mathbf{-}\mathit{N}$ 400.0 N. You want to place a small weight on this bar.

(a) What is the heaviest weight you can put on without breaking either cable, and

(b) where should you put this weight?