Classical Mechanics Answers

A light rod of length L and a little weight of mass m make up the pendulum. In a vertical plane, the rod can complete a full rotation. The weight is initially in the bottom equilibrium position. A horizontally directed velocity v is applied to the weight. What values of v will cause the pendulum to oscillate, and what values will cause it to rotate in the vertical plane? At what starting velocity v will the rod be crushed at the top point, and at what initial velocity v will it be stretched?

A thin uniform rectangular plate (lamina) is of mass m and dimensions 2a by a. Choose a coordinate system Oxyz such that the plate lies in the xy plane with origin at a corner, the long dimension being along the x-axis. Find the following. (a) The moments and products of inertia. Express your results in the form of the inertia tensor. (b) The moment of inertia about the diagonal through the origin. (c) The angular momentum about the origin if the plate is spinning with angular rate ω about the diagonal through the origin. (d) The kinetic energy in part (c).

A uniform solid ball has some turns of light string wound around it. If the end of the string is fixed and the ball is allowed to fall under gravity, what is the acceleration of the center of the ball?

1. How does density affect pressure in liquids?

2. How pressure vary with dept?

3. How does water pressure increase with dept?

4. Does presure depends on density?

Two systems are transitioned from State A to State B through different processes. Process 1 takes the system from state A to state B at a higher pressure than process 2.

How does the change in internal energy compare for both processes

A)  process 1 has a smaller change in internal energy 

B) both processes have the same change in internal energy

C) not enough given to decide 

D) process 1 has a bigger change in internal energy 

Calculate the final equilibrium temperature when 150 grams of 23 degrees Celsius water are mixed with 50 grams of ice at 0 degrees Celsius. The specific heat of water is 4186J/Kg C and the heat of fusion for water is 334 Kj/kg

Find the magnitude and direction of the vector represented by the following pairs of components:

(a) Ax = -8.60 cm, Ay = 5.20 cm; (b) Ax = -9.70 m., Ay = -2.45 m; (c) Ax = 7.75 km, Ay = -2.70 km.

 Find the center of mass of each of the following: (a) Athin wire bent into the form of a three-sided, block-shaped "Ll"with each segment of equal length b (b) A quadrant of a uniform circular lamina of radius b (c) The area bounded by parabola y =x2/b and the line y =b (d) The volume bounded by paraboloid of revolution z = (x2 +y2)/b and the plane z = b 

Show that energy transferred by energetic electron to helium atom by elastic collision is less than 0.1%.

A = -2î +6ĵ & B = 2î - 3j