(a) Explanation Given information: The mass of the sphere ( m ) is 0.6 kg . The spring constant ( k ) is 100 N / m . The magnitude of the velocity at A ( v A ) is 20 m / s . The distance between the point O to point A ( r A ) is 0.5 m . The velocity at A is inclined at an angle ( θ ) is 60 ° . The central force ( F ) is 80 r 2 . The acceleration due to gravity ( g ) is 9.81 m / s 2 . Calculation: Show the figure of the elastic cord with the velocity as in Figure (1). The distance from the point O to point B is maximum when the minimum velocity is at B whereas the distance from the point O to point C is minimum when the maximum velocity is at C . Use the principle of conservation of angular momentum at positions A and A ′ . Write the expression for the conservation of angular momentum as follows; r A m v A sin θ = r m m v m r A v A sin θ = r m v m Substitute 20 m / s for v A , 0.5 m for r A and 60 ° for θ . ( 20 m / s ) ( 0.5 m ) sin 60 ° = r m v m v m = 8.66 r m (1) Consider the point A . Calculate the kinetic energy at the point A ( T A ) using the formula: T A = 1 2 m v A 2 Substitute 0.6 kg for m and 20 m / s for v A . T A = 1 2 × ( 0.6 ) × ( 20 2 ) = 120 J Calculate the potential energy at the point A ( V A ) using the formula: V A = ∫ F d r Substitute 80 r 2 for F . V A = ∫ 80 r 2 d r = 80 [ r − 2 + 1 − 2 + 1 ] = 80 ( r − 1 − 1 ) = − 80 r Substitute 0.5 m for r A . V A = − 80 0.5 = − 160 J Consider the point B . Calculate the kinetic energy at the point B ( T B ) using the formula: T B = 1 2 m v m 2 Substitute 0 (b) To determine Find the corresponding maximum ( v max ) and minimum velocity ( v min ) from the sphere to the origin O .

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 13.2, Problem 13.99P

(a)

To determine

Find the maximum (rmax) and minimum distance (rmin) from the sphere to the origin O.

(b)

To determine

Find the corresponding maximum (vmax) and minimum velocity (vmin) from the sphere to the origin O.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 13.98P

Chapter 13.2, Problem 13.100P

Students have asked these similar questions

Two blocks are free to slide along the frictionless wooden track shown below. The block of mass m, = 4.98 kg is released from the position shown, at height h = 5.00 m above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass m, = 9.20 kg, initially at rest. The two blocks never touch. Calculate the maximum height to which m, rises after the elastic collision. m An object of mass 3.07 kg, moving with an initial velocity of 4.98 î m/s, collides with and sticks to an object of mass 3.07 kg with an initial velocity of -4.07 j m/s. Find the final velocity of the composite object. 5) m/s

Problem 1. noticed that the mass m₁ = The system is released from rest with no slack in the cable and with the spring unstretched. It is cylinder, m₂ = 3 kg and the spring stiffness, k = 150 N/m. 4 kg travels up the incline before it comes to rest. Consider the mass of the hanging m2 a. Draw the free body diagrams of both the 4-kg and 3 kg masses denoting all the effective external forces and determine which forces are active and which one are reactive. b. Based on conservation of mechanical energy, determine the distance s traveled by the 4-kg cart before it comes to rest. Assume no mechanical interference and no friction FBQ W=mg (active) T (reachin k = 150 N/m www m₁ = 4 kg 25° P (ructure) m₂ = 3 kg

The contraption shown below consists of two masses connected by a string of negligible mass through a massless pulley. A spring with constant k is placed so that its equilibrium position is located a distance h below the bottom of mass m2. There is no friction either in the pulley or between the surfaces of the masses and the platform. When the two masses m¡ and m2 are released from rest, mass m2 begins falling and pulls mass m¡ up the ramp. a) Find an expression for the maximum compression of the spring d caused by mass m2 when it hits the spring. Your answer should be in terms of the m2 variables given (and g). b) On the axes below, make sketches of the kinetic energy (K), gravitational potential energy (Ugav), and elastic potential energy (Ua) of the system as a function of the height of m2, where y = 0 is defined as the point where mass m2 collides with the spring. Note that the left- hand edge of the axis is the height h, and the right-hand edge of the axis is the height -d. -d…

Chapter 13 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - Prob. 13.2P Ch. 13.1 - Prob. 13.3P Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - 13.6 In an ore-mixing operation, a bucket full of...Ch. 13.1 - Prob. 13.7P Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - Prob. 13.9P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the maximum ( r max ) and minimum distance ( r min ) from the sphere to the origin O .

Solution Summary: The author shows the figure of the elastic cord with the velocity as in Figure (1).

Videos

Find the maximum (rmax) and minimum distance (rmin) from the sphere to the origin O.

Find the corresponding maximum (vmax) and minimum velocity (vmin) from the sphere to the origin O.

Want to see the full answer?

Chapter 13 Solutions