Three cars are approaching an intersection. Car #1 has mass 1500 kg and is driving East at 10 m/s. Car #2 has mass 2500 kg and is driving North at 20 m/s. Car #3 has mass 2000 kg and is driving South at 30 m/s.

a) If the three cars collide simultaneously and stick together, what is their final velocity (magnitude and direction)?

b) What fraction of the initial kinetic energy is lost in the collision?

c) If the collision last 0.5 seconds, what is the magnitude of the average force exerted on car #1? You may neglect any effects of friction between the cars' tires and the road during the collision.

d) If the coefficient of kinetic friction between the cars' tires and the road is uk=0.3, how far do the cars skid after the collision, before coming to rest?

please show the steps on how to solve each step.

An as-wound helical-coil compression spring with infinite fatigue life is needed to resist a dynamic load that varies from 8.0 to 24.0 lbf at 45.0 Hz over a dynamic deflection of 0.3 in. Because of assembly considerations, the solid length of the spring cannot be more than 1.2 in. The spring should have squared and ground ends and is to be made from peened music wire. Upon closure, use a design factor of 1.2 guarding against yielding and a fractional overrun to closure x = 0.15. The fundamental critical frequency should be greater than 10 times the frequency of the dynamic load. The springmaker has the following wire sizes in stock: 0.059, 0.063, 0.072, 0.075, 0.085, and 0.090 in. Select a suitable spring with a fatigue design factor of 1.9 using the Goodman-Zimmerli fatigue failure criterion. Calculate the cost of the wire from which the spring is wound and use it as the figure of merit for your selection

48.

{Exercise 4.31 (Algorithmic)}

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.7 and P(B) = 0.3.

If an amount is zero, enter "0".

1. What is P(A  B)?
   
   
2. What is P(A | B)?
   
   
3. Is P(A | B) equal to P(A)?
   - Select your answer -YesNoItem 3
   
   Are events A and B dependent or independent?
   - Select your answer -Events A and B are dependentEvents A and B are independentEvents A and B could be either dependent or independentItem 4
   
4. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
   - Select your answer -YesNoItem 5
   
5. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
   - Select your answer -Mutually exclusive events are dependentMutually exclusive events are independentMutually exclusive events are either dependent or independent

STAT_14_3

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability that a random bead will be red is 0.3. The probability that a bead will be transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5

A. Remove 8 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly two of them will be red?
B. Take beads out of the box accidentally and on return (sampling with replacement) until you first remove a transparent bead.
1. What is the probability that more than 4 beads will be removed?
2. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?
C. Remove 10 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

STAT_14_3

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability that a random bead will be red is 0.3. The probability that a bead will be transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5

A. Remove 8 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly two of them will be red?
B. Take beads out of the box accidentally and on return (sampling with replacement) until you first remove a transparent bead.
1. What is the probability that more than 4 beads will be removed?
2. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?
C. Remove 10 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

Laptop computers are charged using laptop chargers (adapters) which are connected to 240 V supply and uses 1.5 A to provide 19 V to a computer. Describe in detail, how does adapter convert at 240 V supply to 19 V as output? Does this laptop adapter belong to step up or step down? Justify. What will be the output current if its efficiency is 96% ? The adapter uses low voltages like 240 V, 50 Hz whereas transmission lines operate at very high voltages. How it can be achieved? Inside the computer, A 50 Ω resistor and 100 μF capacitor are connected in series to a 50 Hz source. What will be the maximum voltage in the circuit if r.m.s current in the circuit is 0.3 A? Can you show that the sum of rms voltage across resistor and that across capacitor is more than rms voltage across entire circuit? Compare the phase angle for the above circuit with that for a circuit containing only capacitor.

This is a long question that needs to be fully done on paper, scanned and uploaded. Also type in the answer of (a) in the space provided.

A spring is mounted over an air track in such a way that the one end of the spring is fixed and the other is connected to a spring scale. When the spring is stretched to 0.01 m a force of 1 N is registered on the spring scale. The spring is relaxed and a glider of 0.43 kg (resting on the air track) is connected to it. The glider-spring system is then pulled to the right through a distance of 0.01 m. Calculate the following:

(a) The spring constant k. (1 mark)

(b) The period of motion. (1 mark)

(c) The angular frequency. (1 mark)

(d) Calculate the amplitude and phase angle of the spring-glider system, if the initial velocity and position of the glider is 0.3 m/s and 0.72 m, respectively.

(e) Utilize all the information already calculated and set up equations for the displacement, velocity and acceleration as function of time.

1. Suppose the data on today’s and future expected interest rates is given:

a) Calculate today’s interest rates on 2-year, 3-year and 4-year bonds using the expectations hypothesis. Use these yields to construct a yield curve and plot it. What kind of shape does it have?

b) Now, suppose term premiums for 2-year, 3-year and 4-year bonds are 0.2%, 0.3% and 0.4%, respectively. Recalculate today’s interest rates on 2-year, 3-year and 4-year bonds using the liquidity premium theory. Use the yields to plot the yield curve on the same graph as expectations hypothesis yield curve from part (a). What do you notice?

REQUIRED: