WS_3_Energy_Problems

This most likely is made to be a probelm about mx''+bx'+kx=f(t) m = mass b = friction k = spring constant 4. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is atequilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a mediumwhere friction is small, and we assume it is zero. Note that the acceleration due to gravity near theearth’s surface where the experiment takes place can be taken as 32 ft/s2.(a) Suppose that in addition to the conditions described above, a hammer strikes the mass everyπ/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models theforce of each blow to the mass. Find the function x(t) for the displacement from equilibrium infeet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use ofunit step or Heaviside functions and such that in each time window it is a different multiple of the samesinusoidal function.(b) Now assume the same spring-mass…

. A pulley used to transmit power by means of ropes has a diameter of 3.5 m and has grooves of 45° angle. The angle of contact is 160° and coefficient of friction between the ropes and groove sides is 0.3. The maximum possible tension in the rope is 1000 N ad the mass of rope is 1.5 kg per metre length. What is the speed of the pulley in rpm and the power transmitted if the condition of maximum power prevail? 10

A 250 g ball collides with a wall. The figures below show the ball’s velocity and force exerted on the ball by the wall. What is vfx, the final velocity of the ball? Paste the completed Bar Chart below. 1. identify the system 2. draw a quick sketch of the initial state of the object(s) 3. do a momentum bar chart

Differential Equations - Acceleration and velocity models

Find the differential equation of the mechanical system in Figure 1(a) To obtain the differential equation of motion of the mass and spring system given in Fig. 1. (a) one may utilize the Newton's law for mass and spring relations defined as shown in Fig. 1. (b) and (c) use f = cv for viscous friction, where v is the velocity of the motion and c is a constant. Z/////// k M F. F, F F F, F, k EF=ma F = k(x, - x,) = kx (b) (c) Figure 1: Mass-spring system (a), Force relations of mass (b) and spring (c)

LR = 5m, LG = 2.5m and LC = 1.1m Q2. The Skylark family of sounding rockets consisted of a number of variants (denoted Skylark 5, Skylark 7, and Skylark 12 respectively). These are illustrated on Page 3. The data given below is based on that for the rocket motors they used (all manufactured and named by what was Royal Ordinance – now part of Roxel): Raven XI Motor Total mass: 1280 kg Length = LR See Case Table (units are m) Diameter = 0.44 m Goldfinch IIA Motor Total mass: 420 kg Length = LG See Case Table (units are m) Diameter = 0.44 m Cuckoo IV Motor Total mass: 242 kg Length = LC See Case Table (units are m) Diameter = 0.44 m The payload mass which is additional to the motor masses is to be taken as 100 kg. (a) For the configurations of the three rockets shown on Page 3 in Fig. Q2: (i) Determine the Pitching/Yawing moment of inertia of each rocket about the base of each rocket. (ii) Explain how you could then find the the Pitching/Yawing moment of inertia of each rocket about its…

This the problem how they give it to me I need help please quick

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! Required information The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 2, and the number of blades n. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 rev/min. What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 10 m/s at 2000 m standard altitude? At 2000 m altitude, p = 1.0067 kg/m3. At sea level, p= 1.2255 kg/m3. The power developed is ]KW.

A fender is mounted on a automobile though dampers (to absorb collision energy) and springs (so that the fender can recover after low-speed collisions). During a crash-test, the automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The springs that mount the fender have a stiffness, k, of 1,000,000 N/m. y m barrier 1) Write a differential equation for the deflection of the springs when the fender is in contact with the barrier. 2) If the damping coefficient, c, is 30,000 N-s/m, what is the damping ratio of the mass-spring-damper system when the fender is in contact with the barrier? 3) For that damping coefficient, make a reasonably accurate sketch (with properly labeled axes) of the time-course of the force exerted on the barrier, starting from the moment of first contact. 4) Is there any value of the damping coefficient, c, that would yield no rebound of the vehicle from…

- [-/1 Points] DETAILS SERCP8 4.P.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A freight train has a mass of 1.4 x 10 kg. If the locomotive can exert a constant pull of 8.4 x 105 N, how long does it take to increase the speed of the train from rest to 76 km/h? min Need Help? Read It

[Level 2] Block A (ma = 3 kg) is pulled along a frictionless horizontal surface by a force F = 50 N applied at an angle 0 = 30° with respect to the ground. Block B (mg = 5 kg) is attached to A by an inextensible cable, and the block slides on top of a rubber mat, nailed onto the sur- face, with a coefficient of friction u = 0.6. Find the system's 3.1.19. %3D acceleration and the tension in the cable. F ЕЗ.1.19

I’m struggling with questions a b c

A forensic scientist test-fires a projectile (mass mP) at a cubic block (volume V), made from wood (density D), resting on a rough surface (static = kinetic coefficient uS). The bullet enters the block with an initial velocity vo and exits the block with a velocity v1. The friction forces on the bullet as it passes through the length of the block are unknown and are assumed to be constant. Solve these problems algebraically first: a) What is the deceleration of the bullet inside the block? How many "g" is that? b) How much time does it take the projectile to pass through the block? c) What is the velocity of the block as the bullet exits? d) How long (time) and how far (distance) does the block slide after the bullet has exited? e) Solve the above numerically for the following parameters (g =9.81m/s^2): mP = 10g, V = 0.1m^3, D = 500kg/m^3, µS = 0.8, v0 = 500m/s, v1 = 100m/s

Si Known values: G P R m 1 8 2600 lb 1.4 ft 1.3 slug 0.004s gravity Problem Statement: The horizontal impact force P is applied as pictured for 1 seconds to a thin disk. The object rolls in-plane on a frictionless surface. The dimension "h" is specially selected so that the rolling is without slip because the rotation matches the translation, even though there is no friction. *Physically, a horizontal resultant force is possible through a combination of normal and frictional forces at the point of application. Symbolic Answer: (no units) In terms of any or all of the variables P, R, m, t, and g, find an expression for the value of that causes this special behavior: Numerical Answer: (include units) The angular velocity of the assembly after the force P is applied for f seconds: Be sure to include units with your answers. (counterclockwise positive)

1. A massless spring (k=400) is pulled by 25cm from its natural length and then released,the spring is attached to a 0.40kg block and oscillates across a horizontal frictionlesssurface. Calculatea. Max velocityb. Max accelerationc. Velocity, restoring force and acceleration at 20 cm from its natural length.

The right answer should be F_lift= 105 kip and F_thrust= 415 kip. I tried many times with acceleration in horizontal but couldn’t get these correct numbers.

Pitch direction A baseball pitcher throws a curveball by spinning and throwing the ball, and the schematic diagram shows the stylized pattem of air flow around the ball on a horizontal plane. As the ball travels in the air, it also spins, causing the air flow velocity on the right of the ball, Vz, to be lower than the air flow velocity on the left, VL. The air has density, p. Air flow around the ball p-12 kg/m VR 15 m/s V 18 m/s g-9.81 m/s Spin direction (a) Which way will the baseball curve? To the left, or to the right? (b) Use Bernoulli's cquation to estimate the magnitude of pressure difference between the left and right sides of the ball, that causes the ball to curve. VL VR

2 A metal block of mass m = 10 kg is sliding along a frictionless surface with an initial speed Vo, as indicated below. The block then slides above an electromagnetic brake that applies a force FEB to the block, opposing its motion. The magnitude of the electromagnetic force varies quadratically with the distance moved along the brake (x): 10 FEB = kx², with k = 5 N m² V₁ = 8 m/s m = 10 kg FEB Frictionless surface Electromagnetic brake ⇒x Determine how far the block slides along the electromagnetic brake before stopping, in m.

Data has been gathered from a lifting system used to transport engine parts. The system consists of a drum and cable. The following data was obtained when the drum lowers the load (assume constant acceleration). Drum diameter = 0.8m Mass of load = 3kg Initial velocitv = 0 m/s Time to descend = A secs 2. ( Distance travelled = 0.25m You have been asked to use this information to determine with 4 s.f. accuracy: Drum Cable a) The final linear velocity of the load b) The linear acceleration of the load Load c) The final angular velocity of the drum d) The angular acceleration of the drum e) The tension force in the cable f) The torque applied to the drum In determining the above quantities, you should clearly state the formulae used and apply dimensional analysis techniques to show that all values/units used are homogeneous.

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