Fluid Mechanics: bouyance, harmonic motion, period

Consider an object with height h, mass M, and uniform cross sectional area A floating upright in a liquid with density p. a.) Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium. b.) A downward force of magnitude F is applied to the top of the object. At the new equilibrium position, how much farther below the surface of the liquid is the bottom of the object than it was in part (a)? (The assumption that F is small enough for some of the liquid to remain above the surface of the liquid should be made) c) The result from part b should show that if the force is suddenly removed, the object will oscillate up and down in ... click for more

Elasticity

A bar with cross sectional area A is subjected to equal and opposite tensile forces F at its ends. Consider a plan through the bar making an angle θ with a plane at right angles to the bar. a.) what is the tensile (normal) stress at this plane in terms of F, A, and θ ? b.) what is the shear (tangential) stress at the plane in terms of F, A, and θ ? C.) for what value of θ is the shear stress a maximum?

Power

A car maintains a maxiumum speed of 20 meters per second on an uphill road at an angle of 30 degrees. The weight of the car is 10,000 newtons. Determine (a) Power needed to maintain the speed uphill in Kw. (b) Minimum time it will take to accelerate from rest to 30 meters per second on a level road. (c) Max speed it will be able to maintain if the angle is 20 degrees.

Collisons

A car with a mass of 2200 kgm traveling at a velocity of 20 m/sec collides with a parked car. After the collision its velocity is +10 m/sec. If the mass of the parked car is 1200 kgm, determine (a) Speed of the parked car after the collision. (b) Average force exerted on the parked car if the collision time (delta t) =0.1 sec. (c) Total momentum after collision.

Circular momentum

A plane heading due North makes a level turn with a speed of 100 m/s. The angle of the bank is 15 degrees. Determine (a) Radius of the circular path (b) Cetripetal acceleration. (c) Lift force (d) direction of velocity after 30 seconds. (Weight of the plane is 19600 Newtons)