Question: A particle of mass m slides without friction inside a hemispherical bowl of radius R. Show that, if it starts from rest with a small

A particle of mass m slides without friction inside a hemispherical bowl of radius R. Show that, if it starts from rest with a small displacement from equilibrium, the particle moves in simple harmonic motion with an angular frequency equal to that of a simple pendulum of length R. That is, w = √g/R.

Step by Step Solution

★★★★★

3.54 Rating (147 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Referring to the sketch we have Fmg sin and tan R tan ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-M-O-M (33).docx

120 KBs Word File

Students Have Also Explored These Related Oscillations Mechanical Waves Questions!

A small particle of mass m slides without friction in a spherical bowl of radius r. (a) Show that the motion of the particle is the same as if it were attached to a string of length r. (b) Figure...

A conducting rod AB of mass m slides without friction over two long conducting rails separated by a distance l (Fig. 3.88). At the left end the rails are interconnected by a resistance R. The system...

A particle of mass m is projected from point A with an initial velocity 0 v perpendicular to line OA and moves under a central force F along a semicircular path of diameter OA. Observing that 0 r=r...

Please show you work so that I could understand it better and then preform everything on my own. c) What IS the force exerted by the block on the inclined plane Ht that scenario? 301 A curve has a...

This print out should have 19 questions. be within + 3.0% Multiple choice questions may continue on the next column or page - find all choices 007 (part 1 of 3) 10.0 points before answering- A block...

A small rock with mass 0.10 kg is released from rest at point. A, which is at the top edge of a large, hemispherical bowl with radius R=0.60 m (the figure (Figure 1)). Assume that the size of the...

QUESTION 1 Q1 If a Saturn V rocket with an Apollo spacecraft attached had a combined mass of 2.9 x 10 5 kg and reached a speed of 11200 m/s, how much kinetic energy would it have? Choose one 1 point...

Note: To simplify calculations, you may use g = 10 m/s in all problems.V =7.5 m/s Questions 2-4 refer to the following figure: B C - NWAVAN D velocity (m/s) 1. An object is thrown horizontally to the...

In Exercises 1 - 16, plot the point given in polar coordinates and then give three different expressions for the point such that (a) r 0 and 0 (c) r > 0 and 2 9. (20, 3) In...

Let r be a relation on a scheme R and let s 1 and s 2 be relations on a scheme S, where S is a subset of R. Show thatif s 1 is a subset of s 2 , then (r + s 1 ) would be a superset of (r + s 2 ). Is...

Garrett Corporation paid $200,000 to acquire land, buildings, and equipment. At the time of the acquisition, Garrett paid $20,000 for an appraisal, which revealed the following values: land,...

A mathematics education researcher is studying problem solving in small groups. One phase of the study involves pairing a third - grade girl with a third - grade boy. If the researcher wants between...

A machine is working to a specification of 12.58 0.05mm. A study of 50 consecutive pieces shows the following measurements for 10 groups of sample: Construct -R chart and show the calculations. Find...

The Brac University Basketball Team is looking for new players to join the team. The heights of all the try-out participants is known to follow a normal distribution with a mean of 167 cm and a...

Explain the construction and working of Breeder nuclear reactor with the help of neat sketch?

A java program to display three characteristics of four objects using java method. what will be the code ?

In previous years, Cox Transport reacquired 2 million treasury shares at $20 per share and, later, 1 million treasury shares at $26 per share. By what amount will Cox's paid-in capital - share...

2. A _____________________ variable is a procedure-level variable that retains its value after the procedure in which it is declared ends. a. constant b. static c. stationary d. term

Jane's Cookhouse is a popular restaurant located in a scenic setting. The owner of the restaurant has been trying to better understand costs at the restaurant and has hired a student intern to...

Show all the work and timelines A share of common stock has an expected long-run constant dividend 6%, and the most recent dividend D_0, was $5.00. The stock is currently $50 per share. Calculate the...

can anyone help with this question 3. An oil company owns. some land that is purported to contain oil. The company classifies such land into four categories by the total number of barrels that are...