Two soccer players, Mary and Jane, begin running from nearly the same point at the same time. Mary runs in an easterly direction at 4.34 m/s, while Jane takes off in a direction 60.9^o north of east at 5.71 m/s. How long is it before they are 26.7 m apart?

What is the velocity of Jane relative to Mary? Enter first the x-component and then the y-component.

How far apart are they after 3.96 s?

1. a)When applying Newton's 2nd Law to an object on an inclined plane, we choose the coordinate axes parallel and perpendicular to the plane because

it makes the friction force negligible

it means we do not have to split the gravitational force into two components

it makes acceleration along one axis equal to zero

it makes all the forces sum to zero

all of the above

b) The acceleration of an object of mass m down an incline is equal to g*sin(theta)

always

never

only when the mass is light enough to be assumed negligible

only when there is no friction between the mass and the incline

c and d

c) Consider a mass resting on an inclined plane , The magnitude of the normal force

is equal to the magnitude of the weight

is greater than the magnitude of the weight

is less than the magnitude of the weight

is equal to the gravitational field strength, g

a and d

d) A block sitting on an inclined plane starts to slide down the plane when it is inclined at a given angle. To solve foe the coefficient of static friction between the block and the inclined plane, you need:

only the angle

the mass of the block and the angle

the coefficient of kinetic friction

b and c

this is not in the chapter

e) Consider two masses on a frictionless inclined (ideal) Atwood's machine, In order to solve for BOTH the acceleration of the masses and the tension in the string using Newton's second law, we need to know

both masses, the angle, and the normal force

both masses and the angle but not the normal force

both masses but not the angle and not the normal force

it is not possible to solve for both using Newton's second law; an experiment must be done

it is not possible to solve for both using Newton's second law; conservation of energy must be used

Common transparent tape becomes charged when pulled from a dispenser. If one piece is placed above another, the repulsive force can be great enough to support the top piece's weight. Assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a 17.4 mg piece of tape held 0.89 cm above another. (The magnitude of this charge is consistent with what is typical of static electricity.)

7A. Calculations of the primordial material that would form a "quark soup" a few hours after the Big Bang show that the early universe consisted almost entirely of hydrogen (¹₁H = 76 weight %) and helium (⁴₂He = 24 weight %). The present-day atomic ratio of H/He is estimated as 12.5/1. Assuming the present universe consists ONLY of H and He, calculate the present-day wt. % of H and He.

B. Does the present-day wt. % of H and He agree with the Big Bang theory?

C. What physical mechanism(s) explain(s) why the present-day wt. % of H and He does/does not agree with the Big Bang theory?

Intense monoenergetic light source shines on piece of metal. When wavelength of the light is more than 620 nm, no photoelectrons are emitted from metal, and shorter wavelengths begin to produce a flux of photoelectrons. A 248 nm light source is aimed at the same metal, hitting the metal with a power of 0.75 W.

(a) What is the range of energies of photoelectrons produced?

(b) The electrons pass through a single slit, with slit width a= 150 nm and slit perpendicular to the incoming photoelectrons. The photoelectrons travel L=1.5 m before they hit a screen and form an interference intensity pattern. Due to diffraction, what is the width of the MOST energetic photoelectrons on the screen (width = distance between central maximum and first destructive interference)?

Thank you.

You attach a 2.50 kg mass to a horizontal spring that is fixed at one end. You pull the mass until the spring is stretched by 0.500 m and release it from rest. Assume the mass slides on a horizontal surface with negligible friction. The mass reaches a speed of zero again 0.300 s after release (for the first time after release). What is the maximum speed of the mass (in m/s)?

(c7p50) A 1000- kg car collides with a 1300- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 25.0 km/h in a direction of 25 ^o with respect to the positive x axis. The heavier car moves at 28 km/h at -50 ^o with respect to the positive x axis.
What was the initial speed of the lighter car (in km/h)?

Also, What was the initial direction (as measured counterclockwise from the x-axis)?

1. A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0cm. what is the oscillation frequency?

2. A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?

3. An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The spring stretches 2.2cm before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency?

4. A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 570N/m. The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is 0.057m, its kinetic energy is closest to?

Solve by steps and explanation!

A 52.0-kg sandbag falls off a rooftop that is 22.0 m above the ground. The collision between the sandbag and the ground lasts for a total of 17.0 ms. What is the magnitude of the average force exerted on the sandbag by the ground during the collision?

I don't even know where to start... what formulas should I be using?

1. A rock is thrown with an initial vertical velocity component of 30 m/s and an initial horizontal velocity component of 40 m/s.

a. What will these velocity components be one second after the rock reaches the top of its path?

b. Assuming the launch and landing heights are the same, how long will the rock be in the air?

c. Assuming the launch and landing heights are the same, how far will the rock land from where it was thrown?

PLEASE EXPLAIN ALL STEPS AND WHY

Which of the following can change the frequency of a wave? a) interference b) the Doppler Effect c) diffraction d) all of the above

Derive equation Vb=M/m*sqrt2gRcm(1-cos)

An insulated beaker with negligible mass contains liquid water with a mass of 0.275 kg and a temperature of 65.9 ∘C. How much ice at a temperature of -18.7 ∘C must be dropped into the water so that the final temperature of the system will be 34.0 ∘C? Take the specific heat of liquid water to be 4190 J/kg⋅K, the specific heat of ice to be 2100 J/kg⋅K , and the heat of fusion for water to be 3.34×105 J/kg

Chapter 8 Problem 83: A thin hoop of negligible width is rolling on a horizontal surface at speed v when it reaches an incline of angle ?θ. (a) How far up the incline will it go before stopping? (1 point) (b) How long will it be on the incline before it arrives back at the bottom (total time going up and down)? (1 point) (c) The initial speed is 3.0 m/s and the angle is ?=15?θ=15o. Evaluate (a) and (b) numerically. (1 point)