Answered: Show that the variation of gravity with… | bartleby

Related questions

Question

Show that the variation of gravity with height can be accounted for approximately by the
following potential energy function:
V=mp (1-4)
in which re is the radius of the Earth. Find the force given by the above potential function.
From this find the component differential equations of motion of a projectile under such
a force. If the vertical component of the initial velocity is voz, how high does the projectile
go?

Expert Solution

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Consider a block sliding down a plane inclined at an angle to the horizontal. Using Newton's laws, it is straightforward to show that the component of the force along the surface, which we pick to be the x-direction, is: Fx = mg (sin 0 - μK COS 0). (3.59) (a) The block is initially held stationary, but is then released, and starts to move. Using the work energy theorem, calculate the block's kinetic energy, mv², after it has moved a distance d along the inclined plane. (b) Express your answer to (a) in terms of the change in the height of the block, z, instead of d. (c) Interpret your answer to (b), in light of the law of conservation of energy.
Imagine you have a pendulum made of a mass hanging from a spring. Restrict all motion to take place in a vertical plane. At rest the pendulum has length l0. The spring constant is k. There are two degrees of freedom, which you can take as θ, the angle from the vertical of the pendulum, and x, the extension of the spring. Find the generalized force Fθ, and Fx usingthe principle of virtual work.
Find the force corresponding to the potential energy U(x) = (Use the following as necessary: a, b, and x. Express your answer in vector form.) 4b + ,5 -3a F(x) =
A particle, of mass m, is moving in one dimension under the influence of a conservative force with potential V (x). (a) If the potential is given by V (x) = x² – x*, (2) - find any equilibrium points and determine their stability. (b) The particle is started from the origin x = 0 with speed v, and moves under the influence of the potential V (x) defined in equation (2). How large does v need to be for the motion to be unbounded?
In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid bodies that can be treated as particles, the Lagrangian can be defined as: L = T-V where T is the kinetic energy of the particle, and V the potential energy of the particle. It is also advised to start with Cartesian coordinates when expressing the kinetic energy and potential energy components of the Lagrangian e.g. T = m (x² + y² + 2²). To express the kinetic energy and potential energy in some other coordinate system requires a set of transformation equations. 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement - i.e. angle between the string and the perpendicular is given by: 3.2 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 L = T-V = ²² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q. State name the number of generalised coordinates in problem 3.1. Hence write…
A car in an amusement park ride rolls without friction around a track. The car starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle. What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)? If the car starts at height h= 4.50 R and the radius is R1 = 17.0 m, compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter. Compute the radial acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.
As shown in the figure below,a small ball of mass m is attached to the free end of an ideal string of length 7 that is hanging from the ceiling at point S. The ball is moved away from the vertical and released. At the instant shown in the figure, the ball is at an angle ✪ (t) with respect to the vertical. Suppose the angle is small throughout the motion. zero of potential g pivot S 1 m
Use the principle of minimum potential energy developed in Section 3.10 to solve the bar problems shown in Figure P3-52. That is, plot the total potential energy for variations in the displacement of the free end of the bar to determine the minimum potential energy. Observe that the displacement that yields the minimum potential energy also yields the stable equilibrium position. Use displacement increments of O.002 in., beginning with x = -0.004. Let E = 30 x 106 psi and A = 2 in2 for the bars. 10,000 Ib 30 in. 10,000 lb 50 in. (b) Figure P3-52
Find the force corresponding to the potential energy U(x) = −a/x + b/x2.
Answer within 5 minutes
Consider a force in R3 defined by f(x,y,z)=(6*x*y^3, 9*x^2*y^2+2*y,0). Find the potential energy U(x,y,z) such that U(0,0,0)=0.
A box with weight of magnitude FG=2.00N is lowered by a rope down a smooth plane that is inclined at an angle ϕ = 30.0 ∘ above the horizontal, as shown in (Figure 1) at left. The normal force acting on the box has a magnitude n=1.73N the tension force is 1.00 N, and the displacement Δr of the box is 1.80 m down the inclined plane. The work done on the box by gravity is 1.8 J What is the work Wn done on the box by the normal force? What is the work WT done by the tension force?

SEE MORE QUESTIONS