A child bounces in a harness suspended from a door frame by three elastic bands.

(a) If each elastic band stretches 0.200 m while supporting a 6.35-kg child, what is the force constant for each elastic band? (N/m)

(b) What is the time for one complete bounce of this child? (s)

(c) What is the child's maximum velocity if the amplitude of her bounce is 0.200 m? (m/s)

what produces a torque on the boat and what effect does it have on the boat?

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at x_r = 0 and the green car is at x_g = 222 m. If the red car has a constant velocity of 25.0 km/h, the cars pass each other at x = 43.0 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x = 76.3 m. What are (a) the initial velocity and (b) the (constant) acceleration of the green car? Include the signs.

Please show how to Graph the Vector Sets. And Solve for it analytically.

Part A: Experimental Determination of the Equilibrant-

1. Obtain three sets of vectors, two sets of two and one set of three.
2. Use a scale of 1 cm = 10 g. For example, a vector of magnitude 5 cm would be represented by a hanging mass of 50g (5 cm x 10 g/1 cm = 50 g). Record each set of vectors below.

3. Record the value of the equilibrant, mass and angle.

Equilibrant: 142       g @     225      _ for set 1 (Vectors A and B)
Equilibrant:  166              g @  200         _ for set 2 (Vectors A and B)
Equilibrant:     76           g @    60        _ for set 3 (Vectors A, B and C)

Part B: Graphical Determination of Equilibrant-

1. Using the first set of vectors, graphically add the two vectors (using graph paper) to find the resultant.
2. From the resultant, determine the equilibrant. Refer to page 41.
3. Record your results:

Equilibrant:   g @ _ for set 1 (Vectors A and B)
Equilibrant:    g @ _ for set 2 (Vectors A and B)
Equilibrant:   g @ _ for set 3 (Vectors A, B and C)

Part C: Analytical (Mathematical) Addition of Vectors-

1. Calculate the x and y components of each of your vectors and record in the following table.
2. Calculate the magnitude and direction of the resultant R and equilibrant E.

Describe the difference between threshold and non-threshold dose response curves. Give one example of a disease or condition that fall into each category. (2 points)

Galactic Dynamics. Imagine that you are an occupant of a strange, distant galaxy, living on a planet in a solar system 10 kpc away from the galaxy's center. Looking along a galactic longitude of I 25°, you determine the orbital velocity of a cloud to be v = all orbits to be circular. 250 km/s. Take (a) You determine that this cloud is at the subcentral point-what is its orbital radius? (b) What is the mass interior to the cloud's orbit? (c) Observations show that the density is constant in this galaxy out to your radius (10 kpc)-what orbital velocity? is your (d) What is the escape velocity for a star that shares your orbital radius?

Describe how bremsstrahlung and characteristic x-rays are created. Why are there no characteristic x-rays created under 70 kVp? Be thorough in your answer and cover each step in the process (2 points).

Emission lines from the hydrogen Hβ line (rest wavelength of 486.1 nm) are observed in the spectrum of a spiral galaxy at redshift z = 0.9. The galaxy's disk is observed to be inclined at an angle of 45 degrees to the line of sight. The central wavelength of the line is observed to be shifted by 0.5 nm to the red on one side of the galaxy, and by 0.5 nm to the blue on the other side of the galaxy. What is the rotation speed of the galaxy? Hint: you must also account that the redshift expands wavelength differences (Δλ_measured = (1+z)Δλ_emitted)

You throw a ball toward a wall with a speed of 25.0 m/s and a launch angle of 40° relative to the ground. The wall is 22.0 m from the point where you are standing.

1. How far above the release point does the ball hit the wall?

2. What is the velocity as the ball hits the wall?

3. When it hits, has it passed the highest point of its trajectory?

4. At the point where the ball hits the wall, what is the magnitude and direction of the ball of its displacement relative to the release point?

An elevator with mass 500 Kg starts from rest and moves upward 20.0 m in 5.00 s. What is the average rate with which the force from the cable is doing work on the elevator?
g = 9.8 m / s2

A m = 4.0 mg insect has acquired a charge of q = -5.5 nC by flying close to a developing thunderhead. The insect

1.Two balls of mass 5 kg each moving in opposite directions with equal speed say 10 m/s collide head on with each other. Predict the outcome of the collision assuming it to be

Perfectly elastic?

Perfectly inelastic?

Two blocks of masses ?₁ = 700 ? and ?₂ = 1100 ? are connected by a cord of negligible mass and hung over a disk- shaped pulley, as shown in the figure. The pulley has a mass of

? = 1.50 ?? and a radius of ? = 14 ??, and rotates about a light- weight axle through its center. The axle itself is hung from the ceiling by two like cords of negligible mass and is held horizontally. The system is released from rest.

1. Draw a free-body diagram for each of the blocks and the pulley separately. (??)
2. Find the magnitude of the acceleration of the blocks. (??)
3. Find the magnitude of the angular acceleration of the pulley. (??)
4. Find the magnitude of tensions in the cords, ?₁, ?₂, and ?₃. (See the figure.) (??)

You are pulling a rope that is attached to a sled that your cousin is riding on. The rope that you are pulling on is at an angle of 30 degrees above the surface of the snow. Your cousin is holding a second rope that is attached to a second sled that is carrying firewood. The rope that your cousin is pulling is parallel to the surface of the snow. The mass of your cousin and her sled is 45 kg. The mass of the firewood and the sled carrying the firewood is 100 kg. The kinetic friction coefficient between the sleds and the snow is 0.1. Both sleds are speeding up at 0.5 m/s 2. 1.Sketch and label all parameters 2.Draw free body diagrams needed to solve the problems. 3. Determine how much force your cousin needs to pull on the rope attached to the sled with the firewood. 4.Determine the force you are exerting on the rope.