(a) Explanation Given information: The weight of sphere ( W ) is 2 lb. The radius of sphere ( r ) is 3 ft. The friction is negligible. Calculation: Sketch the free body diagram and kinetic diagram of dish as shown in Figure (1). Refer Figure (1). Find the angle ( θ ) making normal force, N to vertical axis using given equation of parabola: y = r 2 6 (1) Here, y is the variation of depth of parabola. Differentiate Equation (1) with respect to x . d y d x = 2 r 6 = r 3 Here, d y d x is the slope of parabola. Substitute tan θ for d y d x and 3 ft for r . tan θ = 3 3 θ = 45 ° Write the general equation of acceleration ( a n ) of dish in rotation a n = v 2 r Apply Newton’s law of equation along y -axis. Σ F y = 0 N cos θ − W = 0 N = W cos θ (2) Apply Newton’s law of equation along n -axis (b) To determine Find the magnitude of the normal force exerted by the sphere on the inclined surface of the dish.

12th Edition

ISBN: 9781265566296

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 12.1, Problem 12.41P

(a)

To determine

Find the velocity (v) of the sphere.

(b)

To determine

Find the magnitude of the normal force exerted by the sphere on the inclined surface of the dish.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 12.39P

Chapter 12.1, Problem 12.42P

Students have asked these similar questions

A thin circular rod is supported in a vertical plane by a bracket at A. Attached to the bracket and loosely wound around the rod is a spring of constant k= 3 lb/ft and undeformed length equal to the arc of circle AB. An 8-oz collar C , not attached to the spring, can slide without friction along the rod. Knowing that the collar is released from rest at an angle 0 with the vertical, determine (a) the smallest value of 0 for which the collar will pass through D and reach point A, (b) the velocity of the collar as it reaches point A.

A 10-lb collar is attached to a spring and slides without friction along a fixed rod in a vertical plane. The spring has an undeformed length of 14 in. and a constant k= 4 lb/in. Knowing that the collar is released from rest in the position shown, determine the force exerted by the rod on the collar at (a) point A, (b) point B. Both these points are on the curved portion of the rod.

The crate/box shown has a square shape, an in-plane size of 10 ft X 10 ft and a uniformly distributed 300 lb weight. It is hung on an overhead roller conveyer and being transported. The crate is at rest when a horizontal force P of 40 lb is applied at the point E, which is 4 ft above the bottom of the box. Knowing that the crate starts to move from rest and at the instant t it reaches a speed of 9.3 ft/s. Neglect the frictions at the hinges A and B and between the rollers and the rail track. Answer the following questions: a) Draw FBD and KD of the box. b) What kind of motion the crate is moving in? c) Write out the motion equations. d) Find the acceleration at the crate's mass center and the pin forces at A and B. e) Determine the distance d and time t of the motion when the speed reaches 9.3 ft/s. A B P 10 ft E 4 ft D + 10 ft

Chapter 12 Solutions

<LCPO> VECTOR MECH,STAT+DYNAMICS

Ch. 12.1 - A 1000-lb boulder B is resting on a 200-lb...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Blocks A and B are released from rest in the...Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Two blocks weighing WA and WB are at rest on a...Ch. 12.1 - Objects A, B, and C have masses mA, mB, and mC,...Ch. 12.1 - Prob. 12.4FBP Ch. 12.1 - Blocks A and B have masses mA and mB,...

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 velocity ( v ) of the sphere.

Solution Summary: The author illustrates how Newton's law of equations is applied along y -axis.