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In a scattering experiment, an alpha particle A is projected with the velocity
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Vector Mechanics For Engineers
- Given that an object with initial velocity v0 has velocity v at a later time t given by v = v0 e −kt for some positive constant k ,→ calculate the position of the object as a function of time, and? [15] ,→ if the object start off from rest and k = 10 s−1 , determine the position of the object afterarrow_forwardA particle P is moving with respect to a stationary reference frame with its position vector defined by a cos(ot) ī+ a sin(at)j + bt k where a, b and are constants and tis time. Derive the expressions of the unit tangential vector, the unit normal vector, and the unit binormal vectorarrow_forwardIn case of emergency, the gas actuator is used to move a 50-kg block B by exploding a charge C near a pressurized cylinder of negligible mass. As a result of the explosion, the cylinder fractures and the released gas forces the front part of the cylinder, A, to move B forward, giving it a speed of 200 mm/s in 0.4 s. (Figure 1) Figure B Part A If the coefficient of kinetic friction between B and the floor is μ = 0.5, determine the impulse that the actuator imparts to B. Express your answer to three significant figures and include the appropriate units. I = 20 Submit MÅ N s Previous Answers Request Answer < Return to Assignment X Incorrect; Try Again; 3 attempts remaining ? Provide Feedbackarrow_forward
- In a totally inelastic collision between a moving object and a stationary object, the two objects will bounce off each other, without losing energy. bounce off each other, losing energy. stick together.arrow_forward(b) A particle moves with a velocity of V= 35 t - 221t +120 Find the distance travelled after 10 s.arrow_forwardGiven the particle motion: x = 3t^3 + 2t^2 + 3t, where x and t are expressed in meters and seconds, respectively. (a).Determine the velocity (m/s) when t=10 seconds. (b). Determine the velocity (m/s) when t=5 seconds.arrow_forward
- In a perfectly non elastic collision, kinetic energy is unchanged Select one: O True O Falsearrow_forwardTwo particles A and B start from rest at the origin s = 0 and move along a straight line such that (1212 - 8) ft/s?, where t is in seconds. Determine the distance between them when 1 = 4 s and the total distance each has traveled in t = 4 s. 2. a A = (61 – 3) ft/s² and ag %3D -arrow_forwardParticles B and A move along the parabolic and circular paths, respectively. B has a velocity of 6 m/s in the direction shown and its speed is increasing at 5 m/s², while A has a velocity of 9 m/s in the direction shown and its speed is decreasing at 7 m/s². Particle A moves so that the same side of it always faces the center of the circle. (Figure 1) Figure 2 m B VB m |y=x² 1 of 1 Part A Determine the x and y components of the relative velocity of B with respect to A using scalar notation. Express your answers using three significant figures separated by a comma. (UB/A)T. (UB/A)y= Submit Part B (aB/A). (aB/A)y= Submit VE ΑΣΦ 41 Request Answer Provide Feedback Determine the x and y components of the relative acceleration of B with respect to A using scalar notation. Express your answers using two significant figures separated by a comma. [5] ΑΣΦ | 1 VE vec Request Answer vec ? Ć B ? m/s m/s²arrow_forward
- Consider a bouncing ball. At time t = 0, the ball is dropped from a height_y(0) = họ, where ho is the initial height in meters. It falls freely. At some later time t₁ it hits the ground with a velocity y(t₁) < 0 m/s (meters per second). A bump event is produced when the ball hits the ground. The collision is inelastic (meaning that kinetic energy is lost), and the ball bounces back up with velocity −ay(t₁), where a is constant with 0 < a < 1. The ball will then rise to a certain height and fall back to the ground repeatedly. The behavior of the bouncing ball can be described by the hybrid system of Figure 1. There is only one mode, called free. When it is not in contact with the ground, we know that the ball follows the second-order differential equation, ÿ(t) = −g, where g 9.81 m/sec². = Bouncing Ball bump y(t) = 0/ bump y(t):= -ay(t) 5 free y(t) y(t)=-8 y(0) := hó y(0) := 0 Figure 1. Illustrate state variables y(t) and y(t), with initial conditions denote y(0) = ho and y (0) = 0.arrow_forwardWhich of the following is the momentum of a 70 g bullet fired at 410.4 m/s? * O 15.20 N's O 28.73 N's O 34.80 N•sarrow_forward7. During impact, particles collide with a very short interaction period. The interparticle impulse during an impact collision includes a deformation impulse as particles undergo some combination of elastic and plastic deformation plus a restitution impulse during which some portion of of the deformation is reversed. The magnitude of the restitution impulse is always greater than that of the deformation impulse. True Falsearrow_forward
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