f 400 m/s travel owing vectors: outh+20 N North + 5 N South s 30° Compass direction + 20 m/s 210° com to the right + 3 m to the top + 6 m to the lef Cartesian system of axes: 9,8 m/s² at 270° + ollowing vectors graphically and find the resul
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- A wooden ballistic pendulum, with a mass equal to 10 kg, suspended by a wire 1 meter long, is hit at t=0 s by a 10 gram bullet, traveling at a speed of 300 m/s, which becomes stuck in it (Use g=9.8m/s2). With respect to the question, consider the following statements. I) The expression that allows to calculate the angle \theta (in rad) between the wire and the vertical as a function of time is \theta(t)=0.096 \sin(3.13\; t). II) The first instant of time in which the pendulum reaches its maximum height is t=1s. III) The maximum angular acceleration is approximately 0.94 rad/s2. It is correct what is stated in Choose an option:I, II and III.I, just.I and II only.II and III only.I and III only.Consider a hollow sphere of radii h and 3h, interior and exterior respectively. The mass density in the sphere is ρ = k / r, Kg / m³, where k is a constant, and r is the distance from the center of the sphere to an arbitrary point within it. If k = 3 m, find the gravitational field of the distribution at a point (P), on the x-axis, located at a distance of 4h, measured with respect to the center of the sphere. Ans: 5.655e-10Find the Following: 1.Keq 2. Ceq 3. Natural angular velocity
- A crank of length 30 cm, starting from an initial horizontal position P, rotates in a positive sense (counterclockwise) at a uniform rate of one revolution per second.a) Determine a function that gives the height of the end of the crank from the initial position line at any time t.1) A cylindrical rod of constant shear modulus, G is of length L and located between z=0 and z=L. It has a polar moment of inertia given by J=(Jo)/(1-Z/L) and t=-sin(πZ/2L)where Jo is a constant.The boundary conditions are dΦ(o)/dz =0 AND Φ(L)=0 Find Φ(z) and graph (1/GJo)Φ(Z), and (1/GJo)(dΦ(Z)/dz) ?A circular saw blade 0.6 m in diameter starts from rest and accelerates with constant acceleration to an angular velocity of 100 rad.s-1 in 20 s. Find the linear velocity of a point in the rim of the saw when the angular velocity is 10 rad.s-1.
- The plate of a record player with a moment of inertia of 0:015 kg m2 rotates freely at 33 rpm. If you slowly drop a 180-gram vinyl disc with a 30:48 cm diameter on the board, what will be the new angular speed? (N.B. In real life, the turntable motor forces the speed to always remain 33 rpm. In this problem, we act as if the engine did not exist. )A 45 grams (0.045 kg) golf ball of diameter equal to 43 mm fell into a 2m deep lake. Neglect inertia at the moment of impact. Assume viscosity of 1.12x10-3 Ns/m2 , water density of 1,000 kg/m3 and Cd=0.5. Sphere volume equals 4π r³ /3. 1. How long will it take from the moment it hits the surface until it gets to the bottom? 2. If one estimates the Cd with Cd=24/Re formula, the settling velocity would be unrealistically large. Why?Which one is not a primary dimension? (a) Velocity (b) Time (c) Electric current (d ) Temperature (e) Mass
- A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 6.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 68 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.1 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. Randomized Variables rp = 8.5 cmrw = 6.5 cmR = 68 cmt = 1.1 s a. Calculate the angular speed of the wheel sprocket ωw, in radians per second. b. Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground. c. If the cyclist wanted to travel at a speed of v2 = 4.5 m/s, how much time, in seconds, should elapse as the pedal makes one complete revolution?The horizontal force due to water acting on the bolt (Fh): Fh=ρ×A1×V1×V1--V2 Fh=1000×π4×0.0752×1.254×1.254+11.286( Fh)=69.472 This is the only part I did not understand how to get. Can you please explain more? I arrived with this equation, -P1A1 - P2A2 (cancelled since atmos. Pres.) +Fh = rho A1v1 (v2-v1) Why did P1A1 disappear in your solution? How did you come up with (v1 - - v2) ? What is the control volume? Why did you not do a summation of forces is equal to change in momentum but instead go immediately to getting the horizontal force acting on the bolt?Angular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…