The unstretched length of a piece of elastic rubber is 5cm a force of 9N is required to stretch if by 1cm.what amount of work will be done to stretch the rubber from a length of 12cm to 8cm if the rubber remained within the elastic limit?
k =9 N/.01 meter = 900 N/m
if you mean from 8 to 12
potential energy at 12 = (1/2) k (.07)^2
potential energy at 8 = (1/2) k (.03)^2
subtract to get Joules required
Thanks
To calculate the amount of work done to stretch the rubber, we need to use the formula for work:
Work = Force × Distance
First, let's find the force required to stretch the rubber from 5cm to 6cm. We are given that a force of 9N is required to stretch it by 1cm. So, to stretch it by 1cm, we have a force of 9N.
To stretch it from 5cm to 6cm, we need 1cm of stretching, so the force required will also be 9N.
Next, let's find the force required to stretch the rubber from 5cm to 8cm. Since we already know the force required to stretch it by 1cm, we can use ratios to determine the force required for 3cm of stretching.
For 1cm of stretching, the force required is 9N. So, for 3cm of stretching, the force required will be (9N/1cm) × 3cm = 27N.
Now, let's calculate the work done to stretch the rubber from 12cm to 8cm.
First, we need to find the force required to stretch it by 4cm. We can use ratios again based on the force required for 3cm of stretching.
For 3cm of stretching, the force required is 27N. So, for 4cm of stretching, the force required will be (27N/3cm) × 4cm = 36N.
Now we have the force and the distance of stretching, which is 4cm. Let's calculate the work done:
Work = Force × Distance
= 36N × 4cm
= 144Ncm
Therefore, the amount of work done to stretch the rubber from a length of 12cm to 8cm is 144Ncm.
To find the amount of work done in stretching the rubber from a length of 12cm to 8cm, we need to determine the change in potential energy due to stretching.
First, let's find the amount of potential energy stored in the rubber when it is stretched by 1cm. The force required to stretch the rubber by 1cm is 9N. Since work is done by applying force over a distance, the work done to stretch the rubber by 1cm is given by:
Work = Force x Distance
= 9N x 0.01m (since 1cm = 0.01m)
= 0.09J (Joules)
Since the elastic potential energy is directly proportional to the square of the elongation or compression, we can calculate the potential energy stored in the rubber when it is stretched by 1cm:
Potential Energy = (1/2) x k x (elongation)^2
= (1/2) x k x (0.01m)^2 (since elongation = 0.01m)
= (1/2) x k x 0.0001m^2 (where k is the spring constant)
Now, let's consider stretching the rubber from a length of 12cm to 8cm.
Change in length = Final length - Initial length
= 8cm - 12cm
= -4cm (the negative sign indicates compression)
To find the change in potential energy, we need to consider the change in elongation:
Change in elongation = Change in length - Original elongation
= -4cm - 5cm (since unstretched length = 5cm)
= -9cm
Now, let's calculate the potential energy change:
Potential Energy change = (1/2) x k x (change in elongation)^2
= (1/2) x k x (-0.09m)^2 (since 1cm = 0.01m)
= (1/2) x k x 0.0081m^2
Since we want to find the work done, and work is equal to the change in potential energy, the work done to stretch the rubber from a length of 12cm to 8cm is:
Work = Potential Energy change
= (1/2) x k x 0.0081m^2 (Joules)
Note: The spring constant 'k' is required to calculate the exact value of work done. Unfortunately, the value of 'k' was not provided in the question.