Please show how calculus can be used in respect to measuring the change of current or wave over a circuit. Please explain how the problem works and what is happening at each step.

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 15.0 ∘ above the horizontal. After it has rolled 4.50 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

9. A cow is standing in a flat field, with its front legs at the distance L from a lone tree. The cow is facing the tree, and the separation between its front and hind legs is D. It is gently raining and the ground is damp, with resistivity ρ. A lightning strikes the tree, for an instant providing a constant current I into the ground. The rest of the problem is concerned with what happens to the cow. (No animals were harmed in the creation of this problem, although unfortunately the situation described here is somewhat realistic.)

(a) Assuming that the current spreads from the base of the tree into the ground (which we will treat as homogeneous) in all three dimensions, calculate the current density at the distance r from the base of the tree.1

(b) What is the voltage between the cow’s front and hind legs?

(c) The cow can sustain a maximal voltage of Vmax between the front and hind legs. What is the minimal distance Lmin that the cow needs to stand from the tree to survive the lightning strike?

A catfish is 4.73 m below the surface of a smooth lake.

(a) What is the diameter of the circle on the surface through which the fish can see the world outside the water?
_____m

A heavy sled is being pulled by two people, as shown in the figure. The coefficient of static friction between the sled and the ground is μs=0.587 , and the kinetic friction coefficient is μk=0.403 . The combined mass of the sled and its load is m=351 kg . The ropes are separated by an angle ϕ=26.0° , and they make an angle θ=30.4° with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving?If this rope tension is maintained after the sled starts moving, what is the sled's acceleration?

Special relativity problems

a)

A windowless spaceship falls freely to the ground along a vertical path. The physicist observes two stationary objects inside the spacecraft, which are at a distance of 1 m from each other when the astronaut is at 100 km altitude. How accurate distance measurement does the physicist need to do to discover that he is not in complete inertia? (Do not take into account the Earth's atmosphere)

b)

Assume that the criterion S moves at a rate v seen from another criterion S. Furthermore, suppose that the initial points of the criteria coincide with time t = 0. Find the Galilei transformation that links the spatial coordinates of the reference systems.

A point charge with charge q1q1 = +5.00 nC is fixed at the origin. A second point charge with charge q2q2 = -6.00 nC is located on the x axis at x = 4.00 m.

1)

Where along the x axis will a third point charge of qq = +2.00 nC charge need to be for the net electric force on it due to the two fixed charges to be equal to zero? (Express your answer to three significant figures.)

37.9 , 45.9 , 41.9, -45.9, are all incorrect

One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 9.0 m/s , they then have the same kinetic energy.

a)What were the original speeds of the two cars?

A fisherman and his young daughter are in a boat on a small pond. Both are wearing life jackets. The daughter is holding a large floating helium filled balloon by a string. Consider each action below independently, and indicate whether the level of the water in the pond R-Rises, F-Falls, S-Stays the Same, C-Can't tell. (If in the first the level Rises, and in the second it Falls, and for the rest one Cannot tell, enter RFCCC)

A) The fisherman lowers himself in the water and floats on his back
B) The fisherman knocks the tackle box overboard and it sinks to the bottom.
C) The daughter pops the balloon.
D) The fisherman fills a glass with water from the pond and drinks it.
E) The daughter gets in the water, looses her grip on the string, letting the balloon escape upwards.

I'm using this to study for an exam, please write out all steps and include formulas, thank you!

The world's fastest land animal, the cheetah, can accelerate at 8.75 m/s² to a top speed of v_cmax = 30.5 m/s. A cheetah observes a passing gazelle traveling at v_g = 19.1 m/s and begins to chase it.

(a) How long, in seconds, does it take the cheetah to reach its maximum velocity, v_cmax, assuming its acceleration is constant?



(b) How far, in meters, has the cheetah traveled, d_max,vel, when it reaches it maximum velocity?


(c) Assume that d is the distance the cheetah is away from the gazelle when it reaches full speed. Derive an expression in terms of the variables d, v_cmax and v_g for the time, t_c, it takes the cheetah to catch the gazelle.


(d) What is the numeric value for this time, t_c in seconds, assuming the cheetah is 32 m away when it reaches maximum velocity?

An object is formed by attaching a uniform, thin rod with a mass of mr = 7.1 kg and length L = 5.28 m to a uniform sphere with mass ms = 35.5 kg and radius R = 1.32 m. Note ms = 5mr and L = 4R.

I have the first couple questions right, but I can't figure out the next one.

The moment of inertia of the object about an axis at the left end of the rod is 1637.1 kg*m^2

If the object is fixed at the left end of the rod, the angular acceleration if a force F = 435 N is exerted perpendicular to the rod at the center of the rod is .7047

*What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

If the object is fixed at the center of mass, the angular acceleration if a force F = 435 N is exerted parallel to the rod at the end of rod is zero.

What is the moment of inertia of the object about an axis at the right edge of the sphere?

An object 2.87 cm high is placed 19.9 cm from a convex mirror with a focal length of 7.70 cm.

(a) Find the position of the image.

Your response differs from the correct answer by more than 100%. cm

(b) Find the magnification of the mirror.


(c) Find the height of the image.

Your response differs from the correct answer by more than 100%. cm

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

(a) q =
What is the relationship between the image distance, the object distance, and the focal length for a mirror? cm

(b) M =  

(c) h' =  
What factors determine the size of the image? cm

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

Show that Hermitian operators have real eigenvalues. Show that eigenvectors of a

Hermitian operator with unique eigenvalues are orthogonal. Use Dirac notation

for this problem.

A child hits an ice cube with a mass of 10 grams on a table with a force of 10 N. The impact lasts 0.02 seconds. The ice cube flies off the table, which is 1 meter high and lands some distance away. Assume there is no friction between the ice cube and the table. a. What is the velocity of the ice cube when it leaves the table? b. What is the final velocity of the ice cube just before it hits the floor? c. What is the momentum of the ice cube just before it hits the floor? d. What distance will the ice cube land from the foot of the table? e. Suppose the ice cube had broken into two pieces just after the child hit the ice and moved away from each other while falling to the floor. How would the total momentum of the two pieces just before they hit the floor compared to the momentum you found in part (c)?

A cooling fan is turned off when it is running at 900rev/min . It turns 1100 revolutions before it comes to a stop.

Part B How long did it take the fan to come to a complete stop?