Chlorophile
  • Study Helper
Badges: 20
Rep:
?
#1
Report Thread starter 6 years ago
#1
Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

EPE=\frac{4mg \times d^2}{2a} since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, \frac{2mgd^2}{a}=mg(a+d) since the change in height will be a+d. Rearranging into a quadratic we get 2d^2-ad-a^2=0 hence (2d+a)(d-a)=0 hence d=-\frac{a}{2} or d=a. Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
0
reply
TeeEm
Badges: 19
Rep:
?
#2
Report 6 years ago
#2
(Original post by Chlorophile)
Question: A particle of mass m is suspended from a fixed point O by a light elastic string of natural length a and modulus of elasticity 4mg. The particle is pulled vertically downwards a distance d from its equilibrium position and released from rest. If the particle just reaches O, find d.

Working:

EPE=\frac{4mg \times d^2}{2a} since the modulus is 4mg, the extension is d and the natural length is a. Since at the highest point all the EPE will be converted into GPE, \frac{2mgd^2}{a}=mg(a+d) since the change in height will be a+d. Rearranging into a quadratic we get 2d^2-ad-a^2=0 hence (2d+a)(d-a)=0 hence d=-\frac{a}{2} or d=a. Since d is greater than 0, d=a. However, according to the mark scheme, d=0.75a. Anyone know where I've gone wrong?
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
2
reply
Chlorophile
  • Study Helper
Badges: 20
Rep:
?
#3
Report Thread starter 6 years ago
#3
(Original post by TeeEm)
I have not checked it but a common mistake at this type of problem is that when string has EPE in the equilibrium position too
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
0
reply
TeeEm
Badges: 19
Rep:
?
#4
Report 6 years ago
#4
(Original post by Chlorophile)
Oh right, that's definitely it. I thought it meant it was pulled a distance d down from its natural length. Thanks!
no worries
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Feeling behind at school/college? What is the best thing your teachers could to help you catch up?

Extra compulsory independent learning activities (eg, homework tasks) (5)
3.73%
Run extra compulsory lessons or workshops (23)
17.16%
Focus on making the normal lesson time with them as high quality as possible (24)
17.91%
Focus on making the normal learning resources as high quality/accessible as possible (19)
14.18%
Provide extra optional activities, lessons and/or workshops (39)
29.1%
Assess students, decide who needs extra support and focus on these students (24)
17.91%

Watched Threads

View All