When a small object approaches a much more massive object, the smaller object can be tidally disrupted. The distance of the closest approach before being tidally disrupted is the Roche limit (recall lecture on rings of plan- ets). If the small object is a star and the large object is a supermassive black hole, the Roche limit is given by

rR= 2.4 * RS * (pBH/p*)^(1/3)

where RS is the Schwarzschild radius, ρ̄BH is the average density of the black hole and ρ̄∗ is the average density of the star.

1. a) Setting the average density of the supermassive black hole equal to its mass divided by the volume contained within the Schwarzschild radius, derive an expression for the mass of a black hole as a function of ρ̄∗ that would have rR = RS.

2. b) If the Sun were to fall into a supermassive black hole, what maximum mass could the black hole have if the Sun would be tidally disrupted before crossing the event horizon (or RS). Compare your answer with typical supermassive black holes in the galactic nuclei.

3. c) If the mass of the supermassive black hole exceeded the mass found above, what would be the implication in terms of the energy release of the infalling star? Could infalling stars effectively power AGNs in this case?

1）On a certain dry sunny day, a swimming pool's temperature would rise by 1.40°C if not for evaporation. What fraction of the water must evaporate to carry away precisely enough heat to keep the temperature constant?

2）A piece of iron block moves across a rough horizontal surface before coming to rest. The mass of the block is 3.3 kg, and its initial speed is 3.2 m/s. How much does the block's temperature increase, if it absorbs 74% of its initial kinetic energy as internal energy? The specific heat of iron is 452 J/(kg · °C).

°C

A load of bricks of mass M = 185 kg is attached to a crane by a cable of negligible mass and length L = 3.19 m. Initially, when the cable hangs vertically downward, the bricks are a horizontal distance D = 1.39 m from the wall where the bricks are to be placed. What is the magnitude of the horizontal force that must be applied to the load of bricks (without moving the crane) so that the bricks will rest directly above the wall?

PLEASE, I NEED CORRECT ANSWERS TO ALL THE QUESTION. THEY ARE MULTIPLE CHOICE QUESTIONS. THANK YOU

A basketball star covers 3.05 m horizontally in a jump to dunk the ball. His motion through space can be modeled precisely as that of a particle at his center of mass. His center of mass is at elevation 1.02 m when he leaves the floor. It reaches a maximum height of 1.95 m above the floor and is at elevation 0.880 m when he touches down again. (a) Determine his time of flight (his "hang time"). (b) Determine his horizontal velocity at the instant of takeoff. m/s (c) Determine his vertical velocity at the instant of takeoff. m/s (d) Determine his takeoff angle.

Choose any 3 questions.

1.) What effect does N have on accurately determining the value of the period? What considerations keep one from allowing N to be very large, for example 1000?

2.) What does it mean for the pendulum to have a small angle? How far does the period (T) of the pendulum differ from the linear model that we used to describe the pendulum as a function of initial angle? Note that for this one you will need to measure the period of a single swing of the pendulum. How can you / did you do this?

3.) How can you investigate the pendulum under the effect of reduced gravity? How might you dilute the effect of gravity on the pendulum?

4.) What are the effects of air friction on the mechanical energy of the pendulum? Study the drop in amplitude of oscillation of the pendulum as a function of time, length, mass, period and initial amplitude.

5.) Define the terms amplitude, frequency, angular frequency, and period as they apply to the pendulum.

In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 38.0 m, and the heights of the Jackson and Walton buildings are, respectively, 15.0 m and 22.0 m. The first balloon launched by the Jackson team hits Walton dorm 2.20 s after launch, striking it halfway between the ground and the roof. Ignore air resistance. (a) Find the direction of the balloon's initial velocity. Give your answer as an angle (in degrees) measured above the horizontal. (b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.

Light weight charged bodies stick to neutral matter. Why?

A QL = -22 ?C charge is placed on the x-axis at x = - 0.4 m. A QR = 22 ?C charge is placed at x = +0.4 m. (for all answers below assume that the unit vector x^ points toward positive x, and y^ points towards positive y.).

a.What is the x-component of the electric field at x = 0 m and y = 0.4m? (N/C)

b. What is the y-component of the electric field at x = 0 m and y = 0.4m? (N)

c What is the x-component of the electric field at x = 0 m and y = -0.4m? (N/C)

d. What is the y-component of the electric field at x = 0 m and y = -0.4m? (N/C)

B and D are 0 but I can't figure out A and C

Exercise 19.
Repeat Exercise 3. with the contestant pulling the block of ice with a rope over his shoulder at the same angle above the horizontal as shown in Figure 5.7(b).

Number of spacecraft that visited both Jupiter and Saturn but neither Uranus nor Neptune:

(Please explain for a rating. Thanks!)

1.WHICH OF THE FOLLOWING IS NOT ONE OF THE FUNDAMENTAL QUESTIONS THAT SHOULD BE ASKED WHEN PLANNING AND CARRYING OUT ACTIVITIES IN A DEVELOPMENTALLY APPROPRIATE CLASSROOM?

A. Is it what the children want at the time of instruction?

B. Is it individually appropriate?

C. Is it socially and culturally appropriate?

D. Is it age appropriate?

2.Which of the following early childhood theorists developed the theory of learning intelligence as it pertains to individual learning styles?

A. Erik Erikson
B. Jean Piaget
C. Maria Montessori
D. Howard Gardner

3. Practice or pre-exercise theories of play pose the idea that

A. play provides children with an opportunity to practice adult activities.

B. play is necessary to reenergize human cognition.

C. children have too much energy and play will rid them of that energy.

D. children are the link between animals and human beings.

4. Direct instruction takes place when

A. Children explore their surroundings and learn based on their own curiosity and interests.

B. Learning takes place through a process of solving a specific problem.

C. The teacher shows children how something works or how to complete an activity.

D. A skill set is explicitly taught or an activity is completed.

5.Which of the following learning styles describes children who have highly developed auditory skills and the ability to use words effectively?

A. Interpersonal

B. Musical

C. Visual=spatial

D. linguistic

6. Exploratory play is best described as

A. the teacher guiding students through a process of discovery that leads to purposeful learning.
B. children being given the time necessary to explore their surroundings, learning based on their own curiosity and interests.
C. learning that takes place through a process of solving a specific problem.
D. the teacher showing children how something works or how to complete a portion of or the entire activity.

You have a resistor of resistance 200 Ω , an inductor of inductance 0.440 H , a capacitor of capacitance 6.10 μF and a voltage source that has a voltage amplitude of 34.0 V and an angular frequency of 250 rad/s . The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit. A-What is the impedance of the circuit? B-What is the current amplitude? C-What is the phase angle of the source voltage with respect to the current? D-Does the source voltage lag or lead the current? E-What is the voltage amplitude across the resistor? F-What is the voltage amplitude across the inductor? G-What is the voltage amplitudes across the capacitor? H- Explain how it is possible for the voltage amplitude across the capacitor to be greater than the voltage amplitude across the source.

A rock climber stands on top of a 50 m -high cliff overhanging a pool of water. He throws two stones vertically downward 1.0 s apart and observes that they cause a single splash. The initial speed of the first stone was 2.2 m/s .

How long after the release of the first stone does the second stone hit the water?

What was the initial speed of the second stone?

What is the speed of the first stone as it hits the water?

What is the speed of the second stone as it hits the water?

Please explain how to solve the equations