Problems with velocity/acceleration involving clock arm

  • Thread starter Combine
  • Start date
  • Tags Tags
    Arm Clock
6 replies · 3K views · last reply
Combine
Messages
14
Reaction score
0

Homework Statement


A traditional watch has a second hand 2.0 cm long, from centre to tip

a. what is the speed of the tip of the second hand?
b. What is the velocity of the tip at 20s? 40s? and 60s?
c. What is it's change in velocity between 15s and 30s?
d. What is it's average acceleration durning the same time interval


Homework Equations


d = v * t
sine law
cosine law
SOH CAH TOA

The Attempt at a Solution


a) used SOH CAH TOA to find the third side of the 90 degree (clock) triangle
cos45 = 2/h
cos45h = 2
h = 4cm (rounded)

v = d/t
v = 4cm / 15s
v = 0.3cm/s

therefore the velocity of the clock arm is 0.3cm/s
****attached is the clock and the final 90 degree triangle****

b) I used the cosine law to TRY to find the other side
due to the clock being on 20s the angle from the start to the ending point of 20s is 120 degrees

C^2 = A^2 + b^2 - 2(2)(2)cos120
c^2 = 8 - 4
C^2 = 4
C = 2

this is where I got stuck
****there is an attachment of the triangle I drew****

thanks to anyone willing to help :D
 
Attachments
  • Hand-drawn triangle with a right-angle mark at the lower left vertex, a vertical side labelled 2cm, a slanted side labelled 2cm, and the angle between them labelled 120.
    traingle.png
    1.4 KB · Views: 505
  • Diagram of a clock face with numbers 1 to 12 and a right triangle from the centre to the 12 and 3 positions, labelled 2cm, 2cm, 4cm, with 45 degree angles marked at 12 and at 3.
    clock.png
    2.8 KB · Views: 505
What is the difference between speed and velocity?
 
the only difference I really see would be that a velocity is a vector while speed is a scalar.
 
What is important is the actual distance that the tip of the second hand travels, not the distance between one location and another (which is displacement, not distance traveled).
 
How far does the tip of the second hand travel in 60 seconds?