Two balls (solid spheres) have the same radius and the same rotational kinetic energy. If the ratio of their masses is

=

, what is the ratio of their angular velocities?

nvm

A mass m = 12 kg rests on a frictionless table and accelerated by a spring with spring constant k = 5249 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μ_k = 0.49. The mass leaves the spring at a speed v = 3.2 m/s.

A)How much work is done by the spring as it accelerates the mass?
B)How far was the spring stretched from its unstreched length?
C)

The mass is measured to leave the rough spot with a final speed v_f = 1.9 m/s.

How much work is done by friction as the mass crosses the rough spot?
D)What is the length of the rough spot?
E)In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from its unstretched length?
F)In this new scenario, what would the coefficient of friction of the rough patch need to be changed to in order for the block to just barely make it through the rough patch?

a 2kg mass lying at rest at the origin is subjected to a force of 10 N directed along the positive X-axis and another force of 10 N along the positive y-axis. How far from the origin will the mass be in 5 seconds?

You have been called to testify as an expert witness in a trial involving a head-on collision. Car A weighs 1515 lb and was traveling eastward. Car B weighs 1125 lb and was traveling westward at 41.0 mph. The cars locked bumpers and slid eastward with their wheels locked for 21.5 ft before stopping. You have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750. How fast (in miles per hour) was car A traveling just before the collision? (This problem uses English units because they would be used in a U.S. legal proceeding.)

A mountain climber jumps a 3.2m -wide crevasse by leaping horizontally with a speed of 7.1m/s . If the climber's direction of motion on landing is -45?, what is the height difference between the two sides of the crevasse?

The position of a 2.75

A rock is suspended by a light string. When the rock is in air, the tension in the string is 45.0 N . When the rock is totally immersed in water, the tension is 29.2 N . When the rock is totally immersed in an unknown liquid, the tension is 21.0 N .

What is the density of the unknown liquid?

A luge and its rider, with a total mass of 84 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 33 m/s. If a force slows them to a stop at a constant rate of 1.1 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force? What are (d)F, (e)d, and (f)W if they, instead, slow at 2.2 m/s2?

When the three blocks in the figure below are released from rest, they accelerate with a magnitude of 0.680 m/s2. Block 1 has mass M, block 2 has 3M, and block 3 has 3M. What is the coefficient of kinetic friction between block 2 and the table?

1. Two capacitors (C₁ = 5.8 uF, C₂ = 14.3 uF) are charged individually to (V₁ = 19.5 V, V₂ = 6.9 V). The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.
   Calculate the final potential difference across the plates of the capacitors once they are connected.

B. Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

C. By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

In the MSUGRA breaking scenario, the stop particle typically appears at energies reachable at the LHC. Other sfermions, notably the partners of up, down, strange and charm are assumed to be degenerate in mass, and also heavier than the stop. Something similar holds for the stau.

Why is the third generation different in MSUGRA (not degenerate as the first two), and why is the mass hierarchy inverted wrt. the Standard Model sector (3rd generation sparticles lighter)?

(I guess these features are not neccessarily specific to MSUGRA, but might apply to more general models as well.)

In cylindrical coordinates, vector A is given as;

A = Aρρ + Aφφ + A_zz .

Vector A is a time-dependent function.

Find the components of d²A / dt² .

A wave in string of linear density 0.13 g/m is given by the equation y(x,t)=0.018 sin (5.64x-6.03 t) in SI units. Calculate the tension in the string.