When a mass m is attached to a spring it exerts a force W = mg on the spring and the length of the spring is changed by delta x. If the single spring is replaced with a) two identical springs in series, what happens to delta xseries compared to the case of a single spring? b) If the single spring is replaced by two identical springs in parallel, what happens to delta xparallel compared to the case of a single spring?

See figure above. Assume all springs are identical, i.e. have the same spring constant k, length, mass, etc. Answer questions a) and b) by stating if delta x increases, decreases or remains unchanged and compare it to the single spring case, i.e. what are delta xseries and delta xparallel in terms of delta x for the single spring case? Hint: Draw a force diagram of the system remembering that the net force on the mass must be zero when it is in equilibrium.

The figure is second from last page of this website: http://www.pa.msu.edu/courses/2015summer/PHY251/labfiles/exp9.pdf

A specific type of ideal gas has a specific heat capacity at constant pressure (c_p=c_v+R) that is a function of temperature T, such that c_p=0.48T+885, where c_p has units of J/kg/K and T has units of K. The gas, which is initially at T1 = 314 K and P1 = 1x10⁵ Pa, undergoes a reversible adiabatic process such that its final temperature is T2 = 772 K. Calculate the pressure of the gas (in Pa) in this final state. Assume the following ideal gas constant: R = 287 J/kg/K. Recall that ds = c_pdT/T – RdP/P

A 50.2-kg skateboarder starts out with a speed of 1.96 m/s. He does 100 J of work on himself by pushing with his feet against the ground. In addition, friction does -279 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 7.11 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give the absolute value.

Two trains, A and B, travel in the same direction on the same set of tracks. A starts at rest at position d, and B starts with velocity v0 at the origin. A accelerates with acceleration a, and B decelerates with acceleration –a. What is the maximum value of v0 (in terms of d and a) for which the trains don’t collide? Make a rough sketch of x vs. t for both trains in the case where they barely collide.

Two boats are heading away from shore. Boat 1 heads due north at a speed of 2.81 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 31.5° north of east at a speed of 1.50 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.29 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?

A 60-cm-diameter, 500 g beach ball is dropped with a 4.0 mg ant riding on the top. The ball experiences air resistance, but the ant does not.

Part A What is the magnitude of the normal force exerted on the ant when the ball's speed is 4.0 m/s? Express your answer with the appropriate units.

I've also looked at other solutions for the same problem and I can't get it right

A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of m_b = 6.5 kg and the sign has a mass of m_s = 16 kg. The length of the beam is L = 2.49 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is θ = 30°.

1) What is the tension in the wire?

2) What is the net force the hinge exerts on the beam?

3)The maximum tension the wire can have without breaking is T = 1025 N.

What is the maximum mass sign that can be hung from the beam?

Starting from rest, a 5 kg block slides 2.5 m down a roughly 30 degree incline. the coefficient of kinetic friction between the block and the incline is uk= .436. Determine a) the work done by the force of gravity, b) the work done by the friction force between the rock and the incline and c) the work done by the normal force. d) qualitatively how would answers change if a shorter ramp at a steeper angle were used to span the same vertical height. Please use neat diagrams + explanations- I'm quite confused. Thank you!!

The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pigeon is flying north at ??,2=17.1vi,2=17.1 m/swhen the eagle swoops down, grabs the pigeon, and flies off. At the instant right before the attack, the eagle is flying toward the pigeon at an angle ?=45.5θ=45.5° below the horizontal and a speed of ??,1=39.7vi,1=39.7 m/s. What is the speed of the eagle immediately after it catches its prey? speed: What is the magnitude of the angle, measured from horizontal, at which the eagle is flying immediately after the strike? magnitude of angle:

1. Stephanie is nearsighted. The farthest object that she can see clearly without using corrective lenses (glasses or contact lenses) is 114 cm away. If she wishes to clearly see an object that is located at infinity (the normal Far Point), she will need to use glasses. What focal length (in cm) will she need for the lenses in her glasses in order to see an object that is located at infinity? Pay attention to the sign conventions for lenses. Make sure that you review the Ray Diagram that shows what happens when a nearsighted eye views a distant object. Do you remember what the basic refraction error is for a nearsighted eye?
What is the Lens Power (in m-1) for this lens?

2. Light from an object enters your eye, is refracted by the lens system (cornea and lens), and an image is formed at the back wall of your eye. This is how we see! Suppose that the distance from the lens system (cornea and lens) to the back wall of your eye is 2.3 cm. If an object is located at 25 cm (the normal Near Point for a healthy eye), what focal length (in cm) is required for the lens system (cornea and lens) in order to create a sharply focused image on the retina? You must keep at least 3 significant digits in your answer. If an object is located at infinity (the normal Far Point for a healthy eye), what focal length (in cm) is required for the lens system (cornea and lens) in order to create a sharply focused image on the retina? During "accommodation", what is the range (in cm) of focal lengths that the lens system (cornea and lens) must have in order to see objects that are located at distances from 25 cm to infinity? In other words, by how many centimeters does the focal length of the eye have to change in order for us to clearly see both nearby and distant objects? You must keep at least 3 significant digits in your answer.

Derive the mutual inductance of primary and secondary coils.

(4.1) A motorcycle and a minivan are at rest, side by side, at a stoplight. When the
light turns green, the motorcycle accelerates at 4 m/s
2 for five seconds, while the minivan
accelerates at 2 m/s
2 for ten seconds. Once each vehicle stops accelerating, it maintains a
constant speed.
(a) Determine the speed of the motorcycle (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s, and
(iv) at t = 12 s.
(b) Determine the speed of the minivan (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s and
(iv) at t = 12 s
(c) Determine the displacement of the motorcycle (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s, and
(iv) at t = 12 s.
(d) Determine the displacement of the minivan (i) at t = 1 s,
(ii) at t = 5 s,
(iii) at t = 10 s, and
(iv) at t = 12 s.

A couple of years ago my son showed an interest in astronomy and we bought a 6" reflector telescope. We use it pretty regularly and have enjoyed it immensely. Lately we've both been wishing we had something bigger to be able see more things and to see what we can see now with more detail.

How do you determine the size of telescope needed to view a certain object?

I understand that there are a lot of other factors that come into play when talking about what you can see and how well you can see it. Ideally I suppose what I'm looking for is some sort of chart/table that gives a general guideline of the scope size and some of the objects that should be viewable (with an average setup).

Are there any such resources?

Derive the equations to find the position, velocity, and acceleration in simple harmonic motions.

An ink droplet with a mass of 1.2E-10 kg and a charge of -1.6E-13 C is moving horizontally at 17 m/s. It then passes between 2 deflection plates. The horizontal length L of these plates is 1.5 cm. There is a uniform electric field of magnitude 1.4E6 N/C, directed downward, between the plates. Everywhere else, the electric field is zero.
a. Calculate the magnitude and direction of the droplet’s acceleration between the plates. Ignore gravity.
b. Calculate the vertical deflection of the droplet when it reaches the end of the plates.