Physics Laboratory Manual
4th Edition
ISBN: 9781133950639
Author: David Loyd
Publisher: Cengage Learning
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Chapter 6, Problem 7PLA
To determine
The instantaneous velocity of particles in the
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Go back to question 6 but this time assume uk=0.2.
a) How much time elapses before the block reaches its maximum height up the plane?
b) How much time elapses from the point it reaches maximum height up the plaane to the point where it was launched?
A/1) In projectiles, why does a particle reach a
velocity of zero? And at what height? Prove it
mathematically. Assume that we have an ideal
conditions of motion. Take the initial velocity
of launching to be v at angle θ from the ground
as shown in figure.
A/2) One day, you were driving a car at a speed of 73.2 km/h and your eyes closed
suddenly for a 0.4 sec. How far does the car move during that time in minutes?
Note: Please answer sections A and B
For a one dimensional system, x is the position operator and p the momentum operator in the x direction.Show that the commutator [x, p] = ih
Chapter 6 Solutions
Physics Laboratory Manual
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- If r and are both explicit functions of time, show thatarrow_forwardCalculate impulse and pulse given: mass: .009072kg max PE: .0889 max KE: .0889 max velocity: 4.42 drop time: .5 s find: impulse? Force? show work so i can understand please and thank youarrow_forwardConsider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. (a) What are the physical dimensions of α and β? (b) Find the general form of r(t), the position of the particle, as a function of time t, assuming the initial position of the particle is r0 = (0, 2, 0) (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot). (c) Show that the speed of the particle is constant, but the acceleration vector a(t) is nonzero. Justify. Assuming the particle has a constant mass m, use Newton’s second law to show that the force acting on the particle is (as a function of the position r = (x, y, z)) F(x, y, z) = mα2(0, −y, −z).arrow_forward
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- As shown in Figure 2, a small square mass m connected to a massless rod moves in a circle of radius r with constant velocity v. In the following, approximate the square mass m as a point mass. a) Express the kinetic energy of the square mass in terms of angular velocity ω, r, and m. (Hint: In circular motion, how is ω related to v?) b) If we express the kinetic energy as K=1/2Iω^2, what is I for System 1?arrow_forwardState how many degrees of freedom the following systems have. In each case indicate appropriate generalizedcoordinates which can be used to describe the motion. (You cannot just say that the generalized coordinatesare “x”, “θ” etc. You should indicate what they are using diagrams.)(a) A particle constrained to move on a planearrow_forwarda) Reverse the Legendre transformation to derive the properties of L(qi, q˙i, t) from H(qi, pi, t), treating the q˙i as independent quantities, and show that it leads to the Lagrangian equations of motion. (b) By the same procedure find the equations of motion in terms of thefunction L' (p, p˙ , t) = −p˙iqi − H(q, p, t).arrow_forward
- Show equations and all work clearly please!arrow_forwardAnwser all questions and each part ! 1. The position function x(t) of a particle moving along an x axis is x = 3.2 − 7.2t2, with x in meters and t in seconds. (a) At what time does the particle (momentarily) stop? (b) Where does the particle (momentarily) stop? (c) At what negative time does the particle pass through the origin? (d) At what positive time does the particle pass through the origin? 2. A car traveling 56.0 km/h is 22.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.13 s later. (a) What is the magnitude of the car's constant acceleration before impact?(b) How fast is the car traveling at impact? 3.The single cable supporting an unoccupied construction elevator breaks when the elevator is at rest at the top of a 189 m high building. (a) With what speed does the elevator strike the ground? (b) How long was it falling? (c) What was its speed when it passed the halfway point on the way down? (d) How long had it been falling when it…arrow_forwardSuppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same height at which it is caught by Ryan. If we ignore air resistance, the horizontal range r of the baseball is a function of the initial speed v of the ball when it leaves Nolan's hand and the angle θ above the horizontal at which it is thrown. Use the accompanying table and the equations below to estimate the partial derivatives. fx(x0,y0)= limΔx→0f(x0+Δx,y0)-f(x0,y0)Δx; fy(x0,y0) =limΔy→0f(x0,y0+Δy)-f(x0,y0)Δy Take a left-hand estimate and a right-hand estimate in each case and give the average of the two as your final answer.(a) Estimate the partial derivative of r with respect to v when v=80ft/s and θ=45∘.arrow_forward
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