Say I rolled a marble down a funnel so that it essentially spiralled into the center and fell through the funnel hole. How would you calculate the number of revolutions around the funnel this marble made before reaching the center of the funnel? I'm using this similarity to find the amount of revolutions an electron would make before it hit the nucleus of a hydrogen, but I can't for the life of me think of a way to calculate number of revolutions of an object traveling in a spiral towards a center.

A horizontal spring with a spring constant of 190 N/cm is compressed 6.3 cm. A wooden block with a mass of 1.5 kg is placed in front of and in contact with the spring. When the spring is released it pushes the block, which slides on a frictionless horizontal surface for some distance. The block then slides up a frictionless incline of 27 above the horizontal and comes to a momentary stop before sliding back down. The system is the spring, the block, the incline, and the Earth. Ignore air resistance. A) Sketch the situation and label all variables for: i. the spring and block before the spring is released ii. the block sliding on the horizontal surface iii. the block sliding up the incline B) List all known quantities. C) Draw the free body diagram for the block sliding up the incline. D) What is the potential energy of the spring before it is released? E) What is the kinetic energy and the speed of the block as it slides on the horizontal surface after the spring has pushed it? F) At what height does the block stop on the incline? G) If the incline were rough, how would the stopping height of the block compare to the stopping height when the incline is frictionless? Explain using energy.

When serving, a tennis player hits the ball horizontally. With a speed of 29.12 m/s. What minimum height, H (in m) from which the ball must be launched to just clear the 0.90 m high net about L = 17.65 m from the server.

How far from the end of the service box (which is a distance of S = 6.80 m from the net) will the ball land if it just clears the net? Use the positive direction if the ball is good (i.e. lands within the service box). Give your answer in meters.

For how long will the ball be in the air? (s)

A 1.9 kg block slides along a horizontal surface with a coefficient of kinetic friction μk = 0.30. The block has a speed v = 1.4 m/s when it strikes a massless spring head-on.

If the spring has force constant k = 120 N/m, how far is the spring compressed?

What minimum value of the coefficient of static friction, μS, will assure that the spring remains compressed at the maximum compressed position?

If μS is less than this, what is the speed of the block when it detaches from the decompressing spring? [Hint: Detachment occurs when the spring reaches its natural length (x=0).]

Explain why the detachment occurs when the spring reaches its natural length (x=0)

Two cars approach an ice-covered intersection. One car, of mass 1.22 103 kg, is initially traveling north at 10.6 m/s. The other car, of mass 1.66 103 kg, is initially traveling east at 10.6 m/s. The cars reach the intersection at the same instant, collide, and move off coupled together. Find the velocity of the center of mass of the two-car system just after the collision.

magnitude

direction_______ north of east

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resis- tance numerically equal to the magnitude of the instanta- neous velocity. If the system is driven by an external force of (12 cos 3t − 8 sin 3t) N, determine the steady-state response.

1. (a) Find the gain function if the external force is f(t) = cos(ωt).

2. (b) Verify that the amplitude predicted by your work in (a) for an ex- ternal force f(t) = cos(3t) is consistent with the amplitude of the response you found in the body of the problem (that they do not match exactly may be attributable to the phase shift in the forcing).

A 110 cm3 box contains helium at a pressure of 1.60 atm and a temperature of 100 ∘C. It is placed in thermal contact with a 220 cm3 box containing argon at a pressure of 3.60 atm and a temperature of 420 ∘C.

A)What is the initial thermal energy of each gas?

B)What is the final thermal energy of each gas?

C)How much heat energy is transferred, and in which direction?

D)What is the final temperature?

E)What is the final pressure in each box?

1. In uniform circular motion, which of the following are constant:

a. speed

b. velocity

c. angular velocity

d. centripetal acceleration

e. magnitude of the net force

If 65.0 L of oxygen at 19.0 ∘C and an absolute pressure of 2.35 atm are compressed to 49.6 L and at the same time the temperature is raised to 58.5 ∘C, what will the new pressure be?

• Consider a liquid of argon (a noble gas) and the liquid of water. Which would have a higher surface tension?  Why?

If you were conducting the wire and compass experiment (Part A) near the equator instead of Oregon, would it be necessary to use more or less wire current to cause the compass needle to deflect? Hint: Consider both components of B_net. Explain your reasoning.

1. A rotating top has a scratch 0.05 m from the vertical axis of rotation. In the time it takes the top to rotate 81 degrees, it rotates __ radians or __ revolutions. Furthermore, the scratch moves a length of arc of __in space. Give your answers to three decimal places.

2. A rotating top has a scratch 0.05 m from the vertical axis of rotation. It increases the angular velocity from 20 rad/s to 40 rad/s in 4 seconds. The angular acceleration of the top is __rad/s^2. The tangential acceleration of the scratch is __m/s^2. Give your answers to two decimal places.

3. A skater is spinning at 2 rev/s. she increases her angular velocity in 7 seconds until it is 8π rad/s. By what angle, in degrees, does she rotate in that time?

4. A skater is spinning at 0.6 rev/s. What angular acceleration is necessary. In units of rad/s^2, to increase her angular velocity to 9 rad/s while she rotates by an angle of 1000 degrees.

2) Momentum and Newton's Second Law: Impulse

(a) A block of wood is struck by a bullet. Is the block more likely to be knocked over if the bullet embeds itself in the wood or bounces back? Explain why. [Hint: in which case is the change in momentum of the bullet (and hence the force applied by the bullet) larger?]

(b) A sudden gust of wind exerts a force of 20.0 N for 1.20 s on a bird that had been flying at 5.00 m/s. As a result, the bird ends up moving in the opposite direction at 7.00 m/s. What is the mass of the bird?

(c) A 144-g baseball is moving toward home plate with a speed of 97mph when it is bunted (hit softly). The bat exerts an average force of 6.50 ×103 N on the ball for 1.30 ms (millisecond). The average force is directed toward the pitcher, which we take to be the positive x direction. What is the final speed of the ball?

How much difference is there between your apparent when standing on flat ground at the equator versus at the south pole? Versus at 60 degree latitude? Assume Earth's radius is 6380 km. What period of rotation for Earth would make you feel weightless at the equator?