The figure shows a pendulum of length L = 2.6 m. Its bob (which effectively has all the mass) has speed v₀ when the cord makes an angle θ₀ = 42° with the vertical. (a) What is the speed of the bob when it is in its lowest position if v₀ = 9.1 m/s? What is the least value that v₀ can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if θ₀ is increased by a few degrees?

A 0.30 kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20 kg puck that is initially moving along the x axis with a velocity of 2.4 m/s. After the collision, the 0.20 kg puck has a speed of 0.8 m/s at an angle of θ = 53° to the positive x axis.

(a) Determine the velocity of the 0.30 kg puck after the collision.
_ at _ ° from +x axis

(b) This was a(n) _ collision since K_f(No Response) K_i

A rescue plane flies horizontally at a constant speed searching for a disabled boat. When the plane is directly above the boat, the boat's crew blows a loud horn. By the time the plane's sound detector receives the horn's sound, the plane has traveled a distance equal to one-third its altitude above the ocean. Assuming it takes the sound 2.02 s to reach the plane, and taking the speed of sound to be 343 m/s, determine the following.

(a) the speed of the plane
m/s

(b) the altitude of the plane
m

A uniform hoop (I = MR2), solid disk (I = 1/2 MR2), and solid sphere (I = 2/5 MR2), each with the same mass and radius, are rolling without slipping, at the same speed on a horizontal surface. The surface they’re rolling on then begins to angle upward. Which of the three objects rolls the least distance up the inclined plane (still assuming that the objects do not slip)?

A The question cannot be answer unless the slope of the inclined plane is known.

B They all go the same distance

C The solid disk

D The hoop

E The solid sphere

1. The angle of an airplane propeller makes with the horizontal as a function of time is given by θ=(125rad/s)t+(42.5rad/s^2)t^2. estimate the instantaneous angular velocity at t=0.00s by calculating the average angular velocity from t=0.00s to t=0.010s

A. Estimate the angular speed at t = 0 by calculating the average angular speed between ti = 0 and tf = 0s.

B. Estimate the angular speed at t = 1.00 by calculating the average angular speed between ti = 1.00 and tf = 1.01s.

C. Estimate the angular speed at t = 2.00 by calculating the average angular speed between ti = 2.00 and tf = 2.01s.

D. Based on the above calculations, is the angular acceleration of the propeller negative, zero, or positive? Explain.

E. Calculate the average angular acceleration from t = 0.00 to 1.00s and from t = 1.00 to 2.00s.

F. Compare the angular acceleration calculated in E with the value of angular acceleration observed in the appropriate coefficient of the original equation for angle as a function of time. If they are not the same, explain why this might be?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(6.18rad/m)x+(702rad/s)t]. Being more practical, you measure the rope to have a length of L and a mass of 0.00333 kg.

Part A Determine the amplitude. Express your answer with the appropriate units. A=

Part B Determine the frequency. Express your answer with the appropriate units. f=

Part C Determine the wavelength. Express your answer with the appropriate units. λ=

Part D Determine the wave speed. Express your answer with the appropriate units. v=

Part E Determine the direction the wave is traveling. Determine the direction the wave is traveling. −x−direction +x−direction

Part F Determine the tension in the rope. Express your answer with the appropriate units.

Part G Determine the average power transmitted by the wave. Express your answer with the appropriate units.

Two loudspeakers emit sound waves along the x-axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x = 0.540m . If speaker 1 is slowly moved forward, the sound intensity decreases and then increases, reaching another maximum when speaker 1 is at x =0.930m .

What is the phase difference between the speakers?

How many 65-W lightbulbs can be connected in parallel across a potential difference of 80 V before the total current in the circuit exceeds 2.0 A ?

Does the sign of the charge of an elementary particle, like an electron or proton, is a more, or less, fundamental property than the "sign" of its symmetry?

REMARKS The negative value of q indicates the image is virtual, or behind the mirror. The image is upright because M is positive.

QUESTION Is the image that a convex mirror produces real or virtual?

The image is always real.It depends on the focal length of the mirror.    The image is always virtual.It depends on the distance to the object.

PRACTICE IT

Use the worked example above to help you solve this problem. An object 3.13 cm high is placed 20.1 cm from a convex mirror with a focal length of 7.70 cm.

(a) Find the position of the image.
cm

(b) Find the magnification of the mirror.


(c) Find the height of the image.
cm

EXERCISEHINTS:  GETTING STARTED  |  I'M STUCK!

Suppose the object is moved so it is 3.85 cm from the same mirror. Repeat parts (a) through (c).

(a) q =  cm

(b) M =

(c) h' =  cm

The image is  ---Select--- upright and virtual inverted and virtual inverted and real upright and real .

17.You launch a projectile at an initial speed of 45.8 m/s from the ground. After 3.30 seconds of flight, the projectile lands on the ground. At what angle above the horizontal was the projectile launched?

18.A projectile is fired from the ground, reaches a maximum height of 56.4 m and lands a distance of 39.0 m away from the launch point. What was the projectile s launch velocity?

Is our society truly facing an "energy crisis", assuming by this term we mean that we are running out of energy? What is happening to our energy resources as a result of the increasing industrialization of the world?

(a)
When 117 J of energy is supplied as heat to 2.00 moles of an ideal gas at constant
pressure, the temperature rises by 2.00 K. Calculate the molar heat capacity at constant
pressure, CP,m and the molar heat capacity at constant volume, CV,m for the gas. By
considering the two heat capacities, determine whether the gas is monatomic or diatomic.

(b)

Explain what isothermal processes and adiabatic processes are, and the differences
between them, taking care to explain the role, or otherwise, of the environment to which the
system under study is exposed.

(c)

A sample of 8.02 × 10−1 moles of nitrogen gas (with γ = 1.40) occupies a volume of
2.00 × 10−2m3 at a pressure of 1.00 × 105 Pa and a temperature of 300K. The sample is
adiabatically compressed to exactly half its original volume. Nitrogen behaves as an ideal gas
under these conditions.

(i) What is the change in entropy of the gas?
(ii) Show from the adiabatic condition and the equation of state that TV (γ−1) remains
constant, and hence determine the final temperature of the gas.

(d) The gas sample is now returned to its initial state and then isothermally compressed to
half its original volume.
(i) Find the change in entropy of the gas.
(ii) What is the change in internal energy of the gas?
(iii) What is the amount of heat transferred from the gas to its environment?
(iv) Calculate the amount of work done in compressing the gas.

Inflation

(a) Why is it puzzling that the observed CMB temperature is almost exactly the same on opposite sides of the sky? How would this result be explained in cosmology theories that do not include inflation?

(b) How does inflation answer the puzzle from part (a)? What other properties of the homogeneous universe does inflation explain?

A spring (k = 100 N/m), which can be stretched or compressed, is placed on a frictionless table. A 5.00-kg mass is attached to one end of the spring, and the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 4.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. (a) Determine the function x(t). (b) Find the magnitudes of maximum velocity and maximum acceleration. (c) Find the total energy of the oscillator. (d) Find the position, velocity, and acceleration of the mass at time t = 3.00 s.