M1, C3 - Elastic Strings & Springs

Question 1

What is the equation for Hooke’s Law

Answer 1

T = λx / l
Where:
x = extension
l = natural length
λ = modulus of elasticity

Question 2

What is the unit for modulus of elasticity (λ)

Answer 2

Newtons (N)

Question 3

Elastic springs PQ and QR are joined at Q to form one long string. PQ has natural length 1.6m and modulus of elasticity 20N, QR has natural length 1.4m and modulus of elasticity 28N. The ends P and R of the long string are attached to two fixed points 4m apart. Find the tension in the combined spring

Answer 3

Tension in PQ and QR is equal
Extension in PQ = x. Therefore extension in QR is x - 1 as 1.4 + 1.6 + x = 4
T = 20x / 1.6 = 28(1-x)/1.4
x = 8/13
T = 100/13N = 7.69N

Question 4

If you have l and x, what is the final length of a spring or string

Answer 4

l + x

Question 5

What is the difference between strings and springs

Answer 5

Springs can be compressed (thrust) or extended (tension)
Strings can only be extended (tension)

Question 6

How does F = ma relate to strings and springs

Answer 6

Tension (T) will make up a component of F (resultant force)

Question 7

One end string of natural length 0.5m and modulus of elasticity 20N is attached to point A. 1.5m vertically beneath A the other end is attached to a mass of particle 2kg. Find the initial acceleration of the particle

Answer 7

F = ma
F = T - 2g
T = (20 * 1) / 0.5 = 40N
F = 20.4
F / m = 20.4 / 2 = 10.2ms^-2

Question 8

How could you find the length of a string when a particle reaches maximum speed

Answer 8

F = ma, a = 0 therefore resultant force = 0
T = downwards forces, solve for T and then work out x and add to l

Question 9

What is the equation for the work done to a spring / string moving it from l to (l + x)

Answer 9

(λx^2) / 2l

Question 10

What is the stored elastic potential energy of a string equal to when stretched from l to (l + x)

Answer 10

EPE = Work Done = (λx^2) / 2l

Question 11

Using Hooke’s law, what is change in energy equal to

Answer 11

Change in energy = work done

Question 12

On a graph of applied force T against extension s, how do you calculate work done

Answer 12

T = λx / l
s = x
Area under curve = work done (J)

Question 13

A light inelastic spring has natural length 0.6m and modulus of elasticity 10N, find the work done in compressing the spring from a length of 0.5m to a length of 0.3m

Answer 13

At 0.5m, EPE = 1/12
At 0.3m, EPE = 3/4
3/4 - 1/12 = 2/3J

Question 14

What is the formula for Ek, Ep and EPE

Answer 14

1/2 mv^2
mgh
(λx^2) / 2l

Question 15

When does the total energy in a system (Ek + Ep + EPE) not remain constant

Answer 15

When there is work done against friction

Question 16

How do we calculate work done against friction

Answer 16

Wd = F x d
Force x distance

Question 17

When dropping a particle attached from a string when is velocity the highest

Answer 17

When the ball is in equilibrium position (at height of l (natural length)) below the drop point
Where Ek is max

Question 18

When trying to keep a particle inclined from the vertical from a set angle x, how do you find the magnitude of least force to keep it there

Answer 18

Magnitude of least force will be perpendicular to the string