Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.80m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.10mm . What is the difference between these wavelengths? in meters

Q1-Assume momentum is conserved in this case.

A cart of mass 0.509kg is moving on a friction balanced track with a speed 0.43m/s. It then collides with another cart of mass 0.546kg that is at rest, and become stuck with it. What is the speed in (m/s) after collision?

Assume momentum is conserved in this case.

Q2-Cart A of mass 0.749kg is moving on a friction balanced track with a speed 0.476m/s. It then collides with cart B of unknown mass which is at rest. After collision, the two carts are stuck together with a speed 0.272m/s. What is the mass of cart B (in unit of kg)?

Q3-Assume momentum is conserved in this case.

Cart A of mass 0.929kg is moving on a friction balanced track with a speed 0.44m/s. It then collides with cart B of mass 0.433kg which is at rest. After collision, cart A's speed slows down to 0.129m/s. What is the speed of cart B in (m/s) after collision?

Q4-

Assume momentum is conserved in this case.

Cart A of unknown mass is moving on a friction balanced track with a speed 0.427m/s. It then collides with cart B of mass 0.407kg which is at rest, becoming stuck together with a speed 0.193m/s. What is the mass of cart A in (kg) after collision?

A block of mass m2 = 15 kg on a rough 30°-inclined plane is connected to a 5-kg mass (m1) by a string of negligible mass passing over a pulley that is shaped like a disk. The 2-kg pulley has radius 15 cm and rotates about its symmetry axis of rotation. The string does not slip on the pulley and causes the pulley to rotate about a fixed horizontal axle through its center of mass. When this system is released from rest, the block (m2) moves at a uniform linear acceleration. The coefficient of kinetic friction between the 15-kg block and the incline surface is 0.10. (a) Find the linear acceleration of the system. (b) Calculate the tension T1, in the string supporting m1, and tension T2, in the string that supports m2. (c) Use energy methods to find the speed of the blocks when the 5-kg block has moved through a vertical displacement of 3 m from rest. (a) [a = 0.56 m/s2]; (b) [T1 = 52.4 N; T2 = 51.8 N]; (c) [v = 1.83 m/s]

A 15 g bullet is fired at 650 m/s into a 4.7 kg block that sits at the edge of a 80-cm-high table. The bullet embeds itself in the block and carries it off the table. How far from the point directly below the table's edge does the block land?

we examined the concept of friction and how it affects everything we do. Air resistance is an important type of friction that you don’t want to forget about as you prepare your post. Consider what the world would be like without friction. For example, in a world without friction, the pitcher in a baseball game can still pitch the ball because he can push off the pitching rubber. The pitching rubber is the rubber slab atop the pitching mound that a pitcher uses to push off to gain velocity. But what happens when the batter swings or when the ball hits the catcher’s mitt?

Now, think of one of your favorite sports or another activity you enjoy. How would the action of that activity be different in a world without friction? In your initial post to the discussion, describe your activity and then respond to the following:

1. Describe at least three ways your activity would change if friction were taken out of the scenario.
2. Does friction make it easier or harder to participate in your activity?
3. What are some advantages and disadvantages that you might encounter if there wasn’t friction in our world?

We often think about two-dimensional motion in terms of a projectile, like someone throwing a ball up in the air. Consider, instead, the surface of an air-hockey table, where the puck travels horizontally from one end of the table to the other. Imagine you’re standing at one end of the table and answer the following questions in your initial post to the discussion.

1. Describe the shape of the puck’s path, starting from the end of the table where you’re standing, as it undergoes the following types of motion:
a. acceleration in the x-direction
b. acceleration in the y-direction
c. constant velocity in the x-direction with acceleration in the negative y-direction

2. What must be true of x-velocity and y-velocity for the puck to travel at a 45-degree angle?

3. How can you make the angle steeper or shallower?

4. Can the puck follow a straight path if it’s accelerating in one or both directions? Choose your own orientation for the coordinate system.

Q1:  Find the final angular velocity if a grinding wheel starts from rest and accelerates at 2 rad/s^2.

Q2:  If the grinding wheel has a mass of 60kg:

a) Find its rotational inertia.

b) Find the torque that produces the acceleration.

c) Find angular momentum at the instant it has rotated for 8s.

I am pretty much lost. Any help will be greatly appreciated.

M1 has a mass of 6.330 kg. It is on a horizontal surface connected by a massless string to a hook where M2 can be increased smoothly. The pulley has a negligible mass & no friction. When M2= 3.266 kg it begins to accelerate downward at a rate of 2.110 m/s2. Calculate u_s - u_k between M1 and the surface.

What is the total power output of our Sun (i.e. the energy output per second)? (a) Assume all of power is released from nuclear reactions, how much mass is the Sun currently losing every second? (b) how many years would it take for the sun to lose 1% of its total mass, if it keeps losing mass at the current rate?

2. A 50 gram steel ball hangs from a 15 cm long string. The ball is brought back to an angle of 15 degrees from vertical at the bottom of the swing it contacts and bounces off the 25 gram ball on a 15cm string. Find the angle of both balls.

There is a typical elliptical galaxy that has a velocity dispersion that is high.

a. relatively, what's its stellar mass?

b. Compared this galaxy to a galaxy with a lower velocity dispersion but the same half light radius. How does the surface brightness of this high σ galaxy differ?

Problem 2 A block of mass 1 kg is sitting on top of a compressed spring of spring constant k = 300 N/m and equilibrium length 20 cm. Initially the spring is compressed 10 cm, and the block is held in place by someone pushing down on it with his hand. At t = 0, the hand is removed (this involves no work), the spring expands and the block flies upwards.

(a)Draw a free-body diagram for the block while the hand is still pressing down. Try to get the forces approximately to scale. The following question should help.

(b)What must be the force (magnitude and direction) exerted by the hand on the block?

(c)How much elastic potential energy was stored in the spring initially?

(d)Taking the system formed by the block and the earth, how much total work is done on it by the spring, as it expands to its equilibrium length? (You do not need to do a new calculation here, just think of conservation of energy.)

(e)How high does the block rise above its initial position?

(f)Treating the block alone as the system, how much net work is done on it by the two external forces (the spring and gravity) from the time just before it starts moving to the time it reaches its maximum height? (Again, no calculation is necessary if you can justify your answer.)

A particle of mass m is confined to a finite potential energy well of width L. The equations describing the potential are

U=U₀ x<0

U=0 0 < x < L

U=U₀ x > L

Take a solution to the time-independent Schrodinger equation of energy E (E < U₀) to have the form

A exp(-k₁ x) + B exp(k₁ x) x < 0

C cos(-k₂ x) + D sin(k₂ x) 0 < x < L

F exp(-k₃ x) + G exp(k₃ x) x > L

Which of the following statements is not correct for this solution?

C cos(-k₂ L) + D sin(k₂ L) = F exp(-k₃ L)

The wave function is continuous at x=0 and x=L    

k_1=sqrt(2m( U₀-E ))/hbar

k₁=k₃

B=0

The first derivative of the wave function is continuous at x=0 and x=L

Write 7-10 sentences describing how the three different types of heat transfer apply to the human body (both externally and internally).  Be sure to describe how this is helpful (or harmful) to our survival. Think about how this changes if we are in an extremely hot or cold environment (both externally and internally).

1. Cecil wants to be able to leap tall doghouses in a single bound while wearing her Super Dog costume. Cecil can almost jump up to the roof of her doghouse now. Cecil thinks that she might be able to retrofit her Rapid Buster Delivery System (which she uses to deposit Buster over the fence when he annoys her) to help her. The basics of her prototype is shown below. A block of mass, m = 5.00 kg is released from a height 5.00 m above the bottom of the track. It carries a very strong magnet and is arranged so as to repel an identical magnet embedded in block m = 10.0 kg initially at rest. The two blocks never touch and friction can be ignored.

1. Calculate the maximum height to which m is returned after the collision. b) What is the flaw in Cecil’s design?

2. What is the flaw in Cecil’s design

2. Next, Cecil and Gretta explore whether inelastic collisions could achieve a puppy escape velocity. They have a 12.0 g was of used chewing gum that they found on a walk and they shoot it at Mark’s 100g candy bar sitting on the table. After impact, the candy bar (covered with gums) slides 7.5m (really long table) before coming to rest. The coefficient of friction between the candy bar and the table is 0.650. What was the speed of the gum immediately before impact?

3. Cecil and Gretta agree that preliminary testing is complete and they are ready for launch! They want to strap Buster to a Saturn V launch vehicle. It consumes fuel and oxidizer at a rate of 1.5 * 10^4 kg/s with exhaust speed of 2.6*10m’s. (a) What thrust would be produced? b) What acceleration is achieved if the initial total mass of Buster plus thruster is 3.00*10^6 kg?