À block of mass m is Im T released from rest on a frictionless surface at a height H above ground level as shown. (a) Find the speed of the block at points A, B, and C. (b) What is the normal force acting on the block at point C? (c) Find H such that the block barely stays in contact with the track at point T. Answer
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released from rest on a
frictionless surface at a
height H above ground
level as shown.
m
T
H
(a) Find the speed of the block at points A, B, and C.
(b) What is the normal force acting on the block at point C?
(c) Find H such that the block barely stays in contact with the track at point T. Answer
in terms of R"
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- The figure below shows a plot of potential energy U versus position x of a 0.76 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 20.0 J, UB = 35.0 J, and Uc = 45.0 J. Uc UB UA 4 х (m) The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? m (b) What are the magnitude and direction of the force on the particle as it begins to move to the left of x = 4.0 m? magnitude direction +X Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (c) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? m (d) What are the magnitude and direction of the force on the particle as it begins to move to the right of x = 5.0 m? magnitude…A 3.6 g marble is fired vertically upward using a spring gun. The spring must be compressed 2.9 cm if the marble is to just reach a target 18 m above the marble's position on the compressed spring. (a) What is the change AU in the gravitational potential energy of the marble-Earth system during the 18 m ascent? (b) What is the change AU in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring constant of the spring? (a) Number (b) Number ogres (c) Number Units Units UnitsA child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop). c)What is the child's final speed, vf in m/s?
- A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop). What is the child's final speed, vf in m/s?Muhammad is running on the road. Find the velocity as a function of displacement x, taking into account the following force functions. so Muhammad mass=M and Let FO and K are positive, and let him start from rest. Then found the potential energy U(x) for these force equations. a) mohumed speeds up as it runs more: Fx = FO + kx b) He runs fast, tires himself, then runs again, repeatedly: (FX = Fo cos(kx))A mass m is acted on by a force F,(x) = Ax' from x = 0 to x = L. (a) If m starts from rest, what is its speed at x = L? (b) Beyond x = L, F, = 0, but the mass encounters a surface with coefficient of kinetic friction 4. How far does m go before coming to rest? [Find the answer using the work-KE theorem.]
- A pogo stick has a spring with a spring constant of 2.5 × 104 N/m, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?The force on a particle is described by 2x^3−6 at a point x along the x-axis. Find the work done in moving the particle from the origin to x=7.A baby is free to move on a horizontal frictionless table and is attracted to the origin by a mysterious force with magnitude F(r) = ar+Br². (i) Find the potential energy function associated with the mysterious force. (ii) If the baby is released from rest at the location (r, 0) = (a, π/4), what will be his speed when he reaches the origin? Law Application a X
- A roller coaster car travels with a speed of 2.29 m/s at point A, located 10.7m above the ground. Calculate how fast the roller coaster is moving when it reaches point D, 10.7m below point A. Assume the roller coaster is ideal and loses no energy to friction.A block of mass 58 kg is dragged at constant velocity by a rope along a horizontal floor. The tension in the rope is 166 N and the rope makes an angle of 25 degrees with the horizontal. Find the coefficient of friction between the block and the floor. Find the work done by the tension on the block after it has been dragged the distance of 7.3 m along the floor.A certain spring is found not to obey Hooke's law; it exerts a restoring force F(x) = -ax² - 6x³ if it is stretched or compressed, where: a = 10.0N/m², B = 300.0N/m³ The mass of the spring is negligible. Calculate the potential energy function U(x) for this spring, if U(x=0) = 0. Find the spring potential energy at x = 0.500 m