8.3.19 Two small masses m₁, m₂ are suspended at the ends of a rope of con- stant length L over a pulley. Find their motion z(t) under the influence of the constant gravitational acceleration g = 9.8 m/sec². Discuss var- ious initial conditions.
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![8.3.19 Two small masses m₁, m₂ are suspended at the ends of a rope of con-
stant length L over a pulley. Find their motion z(t) under the influence
of the constant gravitational acceleration g = 9.8 m/sec². Discuss var-
ious initial conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11c2d8cd-ccd2-4e6b-8a25-f54d1c2b785f%2F15a7141b-43c3-467a-aeb0-4cc1ce3bd567%2Fqeryvrc_processed.jpeg&w=3840&q=75)
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- Problem 9.9 Consider a planet of mass M and radius R. Assume the planet is spherical and has a constant density. By direct integration determine the gravitational field and the gravitational potential at all points inside and outside the planet. (Assume the potential is zero at infinity and there are no other bodies in the universe.)A pendulum consists of a smallobject called a bob hanging froma light cord of fixed length, withthe top end of the cord fixed, asrepresented in Figure CQ7.5. Thebob moves without friction, swingingequally high on both sides. Itmoves from its turning point Athrough point B and reaches itsmaximum speed at point C. (a) Atwhat point does the bob have nonzeroradial acceleration and zero tangential acceleration?What is the direction of its total acceleration at this point?(b) At what point does the bob have nonzero tangentialacceleration and zero radial acceleration? What is thedirection of its total acceleration at this point? (c) At whatpoint does the bob have both nonzero tangential and radialacceleration? What is the direction of its total accelerationat this point?Please asap
- Please solveA 61 kg object experiences a gravitational field of size 2.9 N/kg. Calculate the gravitational force on the object. (Please answer to the fourth decimal place - i.e 14.3225)A mass mm is suspended from a massless spring of natural length 90 cm with the spring constant k=10 Nm-1 and causes the spring to extend by 8.6 cm. Assuming the gravitational field strength g=9.8g, calculate the value of the mass on the spring.
- A simple pendulum is given an initial tangential velocity such that it swings in acomplete circle around its fulcrum. Assume:● The string is 32 meters long● The bob has mass M Determine: (A) The minimum velocity atthe top ofthe loop. Now assume the mass passesthrough the top of the loop with theminimum found in part (a), above; Determine: (B) the velocity at an angle of 30 degrees from the vertical(i.e.: at 30 degrees up from a position fully at the bottom of the loop).Show workThe free-fall acceleration on the surface of Jupiter is about two and one half times that on the surface of the Earth. The radius of Jupiter is about 11.0 RE (RE= Earth's radius = 6.4 x 106 m). Find the ratio of their average densities, Pjupiter/PEarth-
- Consider a roller coaster cart of mass 231 kg. The cart begins at rest at the top of a drop of height 132 m. After doing the drop, picking up a lot of speed in the process, the cart immediately enters a vertical circle of radius 14 m. Calculate the normal force, in N, on the cart at the lowest point in this vertical circle. Use g = 10 m/s2. (Please answer to the fourth decimal place - i.e 14.3225)A point mass m slides without friction from O = (0,0) to P = (a, b) on a curve C under the action of constant gravity (see Figure) with vanishing initial velocity. The time it takes for m to reach P is given by P 1 -ds, Jo T = where ds = V(dr)² + (dy)² and v is the speed. The goal is P=(a,b) y to find the curve C that minimises T. (a) Write T as T = Sº F[y(x), y'(x)]dx and determine the function F. (b) Making use of F – y = const (see Problem 1), derive the relation y' y ƏF dy' V# - 1, where d is a constant. (c) Use the parametric representation y(@) = d sin² = $(1 – cos ø) and determine r(6). %3D The extremal curve is a cycloid.