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?

Together, a pure gold ring and a pure titanium ring have a mass of 13.64 g.13.64 g. Both rings are heated to 85.6 °C85.6 °C and dropped into 11.0 mL11.0 mL of water at 23.3 °C.23.3 °C. The water and the rings reach thermal equilibrium at a temperature of 29.5 °C.29.5 °C.

The density of water is 0.998 g/mL.0.998 g/mL. The specific heat capacity of water is 4.18  Jg⋅°C,4.18  Jg·°C, the specific heat capacity of gold is 0.129  Jg⋅°C,0.129  Jg·°C, and the specific heat capacity of titanium is 0.544  Jg⋅°C.0.544  Jg·°C.

Calculate the mass of each ring.

mass of gold ring: _____g
mass of titanium ring: _____g

A block with mass m = 6.1 kg is attached to two springs with spring constants k_left = 29 N/m and k_right = 48 N/m. The block is pulled a distance x = 0.28 m to the left of its equilibrium position and released from rest.

4) How long does it take the block to return to equilibrium for the first time?

5) What is the speed of the block as it passes through the equilibrium position?

6) What is the magnitude of the acceleration of the block as it passes through equilibrium?

7) Where is the block located, relative to equilibrium, at a time 1.06 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value)

8) What is the net force on the block at this time 1.06 s? (a negative force is to the left; a positive force is to the right)

9) What is the total energy stored in the system?

QUESTIONS Lab Determine the work and the power developed when we walk up the stairs.

1. Will the work increase, decrease or stay the same if we increase the number of steps in the stairs? Please explain.
   
2. Will the work increase, decrease, or stay the same if the student carries heavy boxes
   
3. What can you tell about the energy the student has before and after walking up the stairs? Is it increased, decreased, or stays the same? If the energy changes, can you tell by how much is the minimum change?
   
4. Will the work performed increase, decrease, or stay the same if the student runs instead of walking up the stairs? Please explain.
   
5. What will happen to the power developed if the student runs instead of walking up the stairs? Will the power increase, decrease, or stay the same?

The density of ice is 920 kg/m³. If an ice cube is put in a beaker of water collected from the Great Salt Lake it floats with 80% of its volume submerged. What is the density of the water collected from the Great Salt Lake?

1. 736 kg/m³
2. 1000 kg/m³
3. 1080 kg/m³
4. 1150 kg/m³
5. none of the above

A particle with positive charge q = 9.61 10-19 C moves with a velocity v = (3î + 4ĵ − k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B = (4î + 3ĵ + k) T and E = (3î − ĵ − 4k) V/m. (Give your answers in N for each component.) Fx = N Fy = N Fz = N (b) What angle does the force vector make with the positive x-axis? (Give your answer in degrees counterclockwise from the +x-axis.) ° counterclockwise from the +x-axis (c) What If? For what vector electric field would the total force on the particle be zero? (Give your answers in V/m for each component.) Ex = V/m Ey = V/m Ez = V/m

A spherical rock (R= 19 cm, p=3350 kg/m^3) is attached to the end of a copper wire (diameter 3 mm, effective length of 1.21 m) and then revolved in a circular path in a vertical plane with a period of 0.97 s. Determine the maximum and the minimum length of the copper wire. (You may assume the path remains circular and the motion is uniform).

A long, clear, flexible tube is bent into a U shape (open at both ends), and we pour water into it (density 1000 kg/m3) until the water reaches the same level on both vertical sides. Now we pour a 7 cm tall column of mercury into the left side (density 13,600 kg/m3), which does not mix with the water.

(a) When the fluids reach equilibrium, find the difference in elevation between the top of the mercury (on the left) and the top of the water (on the right). Which end is higher?

(b) Find the difference in elevations if the liquids are reversed, i.e., if the tube is first filled with mercury, then 7 cm of water is poured in at the left end. Which end is higher in this case?

A ring (4 kg, r = 2 m) rotates in a CW direction with initial angular velocity 20 s-1. A disk (8 kg, r = 2 m) rotates in a CCW direction with initial angular velocity 50 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.

What is the initial angular momentum Li of the ring+disk system?

What is the final angular velocity ωf of the ring+disk system?

I've been debating with a classmate about whether weight cause a torque on a sphere of uniform density on a friction-less incline. My perspective is that since the force of gravity acts from the center of mass, if we're considering a sphere then weight will be unable to produce a torque since it will act at the pivot point (the center of the sphere). My classmate contends that the pivot point is actually at the point of contact between the sphere and the surface. So, if this is true the parallel component of the weight would act on a lever arm extending from the point of contact to the center of mass, and therefore cause torque. Can you settle this for me?

Hollywood often portrays bows as extremely lethal. In reality, however, they were being replaced by firearms on the battlefields of Europe already towards the end of the 100 years’ war (1337-1453). While all early projectile weapons were very inaccurate (sights are a recent invention), the most striking difference between the bow and the musket lies in the kinetic energy carried by the projectile. A well trained archer using the famous British Longbow could fire an arrow of about 100 grams (0.1 kg) with an initial energy of approximately 100 J.

QUESTION 1: Compare this to a black-powder musket and a modern rifle. Flintlock muskets typically fired a 30 gram projectile with an initial velocity of 200-300 m/s, whereas a modern US M4 carbine fires a 4 gram bullet at 910 m/s.

QUESTION 2: What would the recoil momentum be for all three weapons?

QUESTION 3: If we assume that the longbow stores energy like a spring, what would the spring constant k be? For simplicity, assume that the displacement is equal to the length of the arrow, which was about 30 inches (0.76 m).

QUESTION 4: In movies and works of fiction skilled archers are sometimes portrayed releasing multiple arrows at the same time. A real archer would, however, never do this. Why?

A ring (mass 2 M, radius 1 R) rotates in a CCW direction with an initial angular speed 2 ω. A disk (mass 4 M, radius 2 R) rotates in a CW direction with initial angular speed 4 ω. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.

What is the initial angular momentum Li of the ring+disk system? Write your answer in terms of MR2ω.

What is the final angular velocity ω_f of the ring+disk system? Write your answer in terms of ω.

List the factors that comprise the image formation model. Describe each briefly.