Beetle on a Pendulum Homework: Solving Displacement & Speed

[Warmacblu]

Homework Statement

A beetle takes a joy ride on a pendulum. The string supporting the mass of the pendulum is 170 cm long.

A) If the beetle rides through a swing of 43 degrees, how far has he traveled along the path of the pendulum?

B) What is the displacement experienced by the beetle while moving through the same angle 43 degrees?

C) If the pendulum at some instant is swinging at 3.3 rad/s, how fast is the beetle traveling?

Homework Equations

theta = s/r

The Attempt at a Solution

A) 43/360 * (2pi * 170) = 127.584 cm - correct

B) s = r(theta)

s = 170 x 43(pi/180) = 127.584 cm - incorrect

C) theta = s/r

3.3 = s/170

s = 561 cm/s - correct

I don't know what I did wrong for part b. Perhaps I am supposed to multiply by pi/360?

 

[Doc Al]

For displacement, imagine an arrow drawn from the starting position to the final position. What's the length of that arrow?

 

[Warmacblu]

For displacement, imagine an arrow drawn from the starting position to the final position. What's the length of that arrow?

sin43 = x/170

x = sin43 x 170

x = 115.9397

 

[semc]

I don't think its a right angle triangle. Maybe cosine rule?

 

[Warmacblu]

I think it might be a right angle because we are taking the angle measurement from the rest position and if I draw and arrow to the right and connect the hypotenuse (170 cm) then the angle turns out to be 90 degrees on the bottom with a 43 degree angle on top.

 

[Doc Al]

I think it might be a right angle because we are taking the angle measurement from the rest position and if I draw and arrow to the right and connect the hypotenuse (170 cm) then the angle turns out to be 90 degrees on the bottom with a 43 degree angle on top.

It's not a right triangle; it's an isoceles triangle with the long sides equal to the length of the string. Hint: Law of sines.

 

[Warmacblu]

It's not a right triangle; it's an isoceles triangle with the long sides equal to the length of the string. Hint: Law of sines.

I looked up the law of sines and law of cosines and I think the law of cosines would be easier to use:

c² = a² + b² – 2abcosC

c² = 170² + 170² - 2*170*170*cos(43)

c = 124.6104

Does that seem okay.

 

[Doc Al]

Looks good.

Using the law of sines, it's just: 170/sin(68.5) = x/sin(43)

 

[Warmacblu]

Looks good.

Using the law of sines, it's just: 170/sin(68.5) = x/sin(43)

Thanks for the help.