Electric Field at a Point

A -70nC charge is distributed uniformly along the x-axis from x = -0.8m to x = 2.6m. Consider a point at y = 1.5m on the y-axis.

a) What is the x-component of the electric field at the point?

b) What is the y-component of the electric field at the point?

c) What is the total magnitude of the electric field at the point?

Thank you

(1)Sphere A is attached to the ceiling of an elevator by a string. A second sphere is attached to the first one by a second string. Both strings are of negligible mass. Here m₁ = m₂ = m = 3.57 kg.

(a) The elevator starts from rest and accelerates downward witha= 1.35 m/s². What are the tensions in the two strings in newtons?

(b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings in newtons?

(c)The maximum tension the two strings can withstand is 92.2 N. What maximum upward acceleration (in m/s²) can the elevator have without having one of the strings break?

(2) Consider the 65.0-kg ice skater being pushed by two others shown in the figure below.

(a)Find the direction (in degrees counterclockwise from the +x-axis) and magnitude (in N) ofF_totthe total force exerted on her by the others, given that the magnitudes F₁ and F₂ are 22.0 N and 15.8 N, respectively. (AssumeF₁points in the positive x direction.)

(b) What is her initial acceleration (in m/s²) if she is initially stationary and wearing steel-bladed skates that point in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(c) What is her acceleration (in m/s²) assuming she is already moving in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(3)Here, m_A = 2.50 kg and m_B = 6.50 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration.

(a) What is the magnitude of the acceleration (in m/s²) of each of the objects?

(b) What is the magnitude (in N) of the tension in the string?

(c)Through what distance (in m) will the two objects move in the first three seconds of motion?

Two thin slits separated by 0.0880 mm are illuminated by light from a He-Ne laser (? = 633 nm), producing interference fringes on a distant screen. Find the angle between the centers of the central bright fringe and the next bright fringe.

How wide would the slits in Young’s two-slit experiment have to become in order for us to end
up in the double slit diffraction situation? Clearly explain your rationale in a maximum of
three succinct sentences.

The table below contains distance and recessional velocity data for ten galaxies.

1. a) Plot the ‘Hubble Diagram’ for these galaxies. This is simply a plot of the observed velocity on the y-axis and the distance on the x-axis.

2. b) Fit a line to the data that goes through the origin of the plot (that is, where the dis- tanceandvelocityarebothzero). TheslopeofthislineistheHubbleconstant.What is the Hubble constant for these data? NOTE: The value is not the same as the Hubble constant we are adopting in the text.

3. c) Calculate the redshift, ? = ∆?/?& for each galaxy. HINT: Go back to the definition of the Doppler effect in Destination 6 to recall what = ∆?/?& is equal to (or just look at question 1c above). You will see that have the information you need in the table above to calculate the redshift (though, strictly speaking, only for redshifts that are significantly smaller than 1.0).

4. d) Notice that galaxies 2-5 in the table are all at about the same distance, but their ve- locities differ rather significantly. Explain what is likely happening to account for this behavior.

A spelunker is surveying a cave. She follows a passage 120m straight west, then 270m in a direction 45❝ east of south, and then 280 m at 30❝ east of north. After a fourth unmeasured displacement, she finds herself back where she started.

One of the most seemingly obvious things in all of our experiences is that the Earth is still and the Sun moves across the sky. And yet, we are told by science, that the Earth is moving not the Sun. How is it that scientists are so certain about this? This is not a quiz! How do you think this certainty came about?

A trooper is moving due south along the freeway at a speed of 33 m/s. At time t = 0, a red car passes the trooper. The red car moves with constant velocity of 45 m/s southward. At the instant the trooper's car is passed, the trooper begins to speed up at a constant rate of 1.5 m/s2. What is the maximum distance ahead of the trooper that is reached by the red car? m

A filament conductor conducts current I in the −az direction and extends along the entire positive z axis. At origin, it is connected to a conductive blade that forms the xy plane. (a) Determine K on the conductive blade. (b) Use Ampère's circuital law to find H for z> 0. (c) Determine H for z <0.

An electron is moving in the field of a helium nucleus (Q = +2e).

1,) What is the change in the electrons potential energy when it moves from a circular orbit of radius 3

Choose one of the following topics and write at least two substantial paragraphs that briefly explain both the topic itself and how the topic relates to our study of light.

The Double-slit experiment
The Photoelectric Effect
Emission spectra of gases composed of a single element

Refraction
Set up the ray box so the light is it directed at the prism at an angle of 50 degrees
Find the value of the prism index of refraction using Snell's law
Find the angle between the ray entering the prism and the ray leaving the prism
Draw a labelled diagram showing your experiment and explain the principle of refraction

A small metal ball with a mass of m = 97.6 g is attached to a string of length l = 1.43 m. It is held at an angle of θ = 42.1° with respect to the vertical. The ball is then released. When the rope is vertical, the ball collides head-on and perfectly elastically with an identical ball originally at rest. This second ball flies off with a horizontal initial velocity from a height of h = 3.26 m, and then later it hits the ground.

At what distance x will the ball land?