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?

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