Vector A has a magnitude of 4 m/s and it is on the positive x axis .

Vector B has a magnitude of 6 m/s and forms a 30 degrees angle with the positive x axis.

Vector C has a magnitude of 8 m/s and forms a 60 degree angle with the negative x axis.

Find:

a) The magnitude of A + B + C = D

Give your answer with two significant figures.

b) The angle vector D form with the x axis.

Give the answer with two significant figures.

c) What quadrant is vector D?

A potential difference of 3.60 V will be applied to a 33.00 m length of 18-gauge platinum wire (diameter = 0.0400inches). Calculate the current.

Calculate the current density.

Calculate the electric field.

Calculate the rate at which thermal energy will appear in the wire.

If 250 g of water is heated by 6 K during the experiment and the water-mass equivalent of the coil is 2.5 g, how many calories of energy has the water (and coil) absorbed? The specific heat capacity (using the archaic units of calories) is: 1 cal/(g K).

a box of mass m = 66.0 kg (initially at rest) is pushed a distance d = 54.0 m across a rough warehouse floor by an applied force of FA = 218 N directed at an angle of 30.0° below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.100. Determine the following. (For parts (a) through (d), give your answer to the nearest multiple of 10.) * I already solved parts b and c so I didn't include them.

a)work done by the applied force WA =

d)work done by the force of friction Wf =

e) Calculate the net work on the box by finding the sum of all the works done by each individual force. WNet = J

f)Now find the net work by first finding the net force on the box, then finding the work done by this net force. WNet = J

A ring of charge with radius 1.5 cm and a charge of 100nC has the electric field along the primary axis of the ring as E=kQx/(R^2+x^2)^3/2

1. find electric field 2.25 cm from the center of the ring along the primary axis
2. what force would a charge of -5nC experience at this point
3. what point charge would you have to place at x=-5cm to make the electric field zero at this location?

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 21.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.37 m/s² for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean.

(a) Find the car's position relative to the base of the cliff when the car lands in the ocean.
m

(b) Find the length of time the car is in the air.
s

A spherical conductor carries a charge −30 μC and has a radius of 20 cm.

a) Determine the electric field and potential at all points in space.

b) Calculate the values of the field and potential at the following points:

i) r = 20 cm, ii) r = 15 cm, iii) r = 40 cm.

The drawing shows an exaggerated view of a rifle that has been ‘sighted in' for a 91.4-meter target. If the muzzle speed of the bullet is v₀ = 475 m/s, there are the two possible angles θ₁ and θ₂ between the rifle barrel and the horizontal such that the bullet will hit the target. One of these angles is so large that it is never used in target shooting. Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identity may be useful: 2 sinθ cosθ = sin 2θ.)

I have been able to get to sin2θ = (9.8m/s^2) (91.4m) / (475 m/s)^2 but i am not sure what to do from here and keep getting the answer wrong.

A rocket is launched from rest and reaches a position of (65m, 185m) and a velocity of (195m/s, 555m/s) when it runs out of fuel. From this time, t_bo, it flies a projectile motion path.

1. Find the maximum height above the ground the rocket achieves after running out of fuel
2. Find the time t and position x of the rocket when it hits the ground.

Multichannel detectors like diode arrays and CCDs provide a signal to noise ratio (SNR) advantage by the ability to measure many wavelengths simultaneously—a multiplex advantage. Consider the SNR for a photomultiplier tube (PMT), a diode array (DA), and a CCD. Assume the readout noise (RN) associated with these devices is 0 photoelectrons (pe^-) for the PMT, 1000 pe^- for the DA and 10 pe­^‑ for the CCD. The readout noise is a constant number that does not change with exposure time, and it adds to other types of noise in the measurement. Assume the only other source of noise in these detectors is shot noise from the signal we are measuring.

When we consider both shot and readout noise, the SNR for a signal S(pe^‑) is given by,

SNR = S/(sqrt[S + (RN)²]).

Assume we want to measure a luminescence signal using a spectrometer that collects a signal of 10⁵ pe^-/s at the detector at every wavelength (e.g., ignore quantum efficiency differences in the detectors, which by the way are in reality very large).

1. What is the signal to noise ratio for a PMT measurement of this luminescence, at a single wavelength, for a 1 second exposure? For a 100 s exposure?
2. How long will it take to measure 1024 wavelengths using the PMT, to give a SNR of 300 at each wavelength?
3. For a 1024-pixel diode array and a 1024x1024 pixel CCD, what total exposure time would be needed to give a SNR of 300 at each wavelength? Note: the readout noise is different for these detectors.
4. Unlike the diode array, the CCD also has pixels in the vertical direction. This gives an additional SNR advantage for the CCD detector. Explain why this is?

A 11.0 nC charge is at x = 0cm and a -1.3 nC charge is at x = 5 cm .

At what point or points on the x-axis is the electric potential zero?

Explain the term ‘strain rate sensitive’. Show your references.

A rope exerts an 18-N force while lowering a 20-kg crate down a plane inclined at 20∘ (the rope is parallel to the plane). A 24-N friction force opposes the motion. The crate starts at rest and moves 11 m down the plane.

Part A:  Determine the final speed of the crate. The system consists of the crate, the surface of the incline and Earth.

Part B: Determine the change in gravitational energy.

Part C: Determine the change in kinetic energy.

Part D: Determine the change in internal energy.

Part E: Determine the work done by the rope.

The parameters that determine the performance of cornstarch as thickener. How to determine these parameters？ What equipment is used in determining these parameters?