Solving Homework: Simple Pendulum & Clock Error

[nns91]

Homework Statement

1. A simple pendulum of length L is attached to a cart that slides without friction down a plane inclined at angle theta with the horizontal. Find the period of oscillation of the pendulum on the sliding cart.

2. A clock with a pendulum keeps perfect time on Earth's surface. In which case will the error be greater: if the clock is placed in a mine of depth h or if the clock is elevated to a height h ? Assume that h<< Radius of earth.

Homework Equations

T=2pi sqrt(L/g)

The Attempt at a Solution

1. So I guess T will not be just normal as 2pi*sqrt(L/g). How does the incline affect the period ? what do I have to calculate ?

2. How should I attack this problem ? I mean does it have to do with gravitational force ??

 

[nns91]

Do I have to use Force in both problems ?

 

[Dr.D]

Start by drawing a free body diagram and writing sum F = ma after you do the necessary kinematics.

 

[nns91]

How will the force affect the period ?

 

[Dr.D]

You have to discover that by working the problem.

 

[nns91]

So mgsin(theta)=ma so a=gsin(theta) so will T=2pi*sqrt(L/g-gsin(theta)) then ?

How about number 2?

 

[Dr.D]

Maybe you ought to lay out the kinematic analysis whereby you got your expression for a.

 

[nns91]

so basically I used Newton's 2nd law F=ma, so the pendulum moves in the x direction so we can ignore the vertical force including tension, then the x component of gravitational force is mgsin(theta). Am I right ?

 

[Dr.D]

You need to re-read your problem statement. You seem to have forgotten what it said about the situation of this pendulum.

Edit: What is happening to the suspension point of this pendulum?

 

[nns91]

What do you think I miss ?

 

[Dr.D]

Evidently just about the whole problem. You need to quite trying to jump to the answer and rather plan to work the problem all the way through.

Draw the picture, then draw separately a FBD for the pendulum, then draw a diagram showing the kinematics needed to describe the motion of the pendulum CM. Then it may begin to sink in on you what is going on here.

Forget all about statements like "so we can ignore the vertical force including tension" and just plan to take EVERYTHKING into account.