The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension x is E. What is thework done by the spring when its extension changes from x to x/4?A. E/16B. E/4C. 3E/4D. 15E/16
Question
The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension x is E. What is thework done by the spring when its extension changes from x to x/4?A. E/16B. E/4C. 3E/4D. 15E/16
Solution
The work done by the spring when its extension changes is equal to the change in the energy stored in the spring.
The energy stored in the spring when its extension is x is E.
When the extension changes to x/4, the energy stored in the spring changes. Since the energy stored in the spring is directly proportional to the square of the extension, the new energy stored in the spring is E/16.
Therefore, the work done by the spring when its extension changes from x to x/4 is E - E/16 = 15E/16.
So, the correct answer is D. 15E/16.
Similar Questions
Suppose that 4 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 47 cm.(a) How much work is needed to stretch the spring from 38 cm to 43 cm? (Round your answer to two decimal places.) J(b) How far beyond its natural length will a force of 20 N keep the spring stretched? (Round your answer one decimal place.) cm
The energy stored U in a spring which follows Hooke's Law stretched a distance x from its normal length is U=12 kx2 , where k is the spring constant and basically describes how stretchy a spring is. Which of the following choices correctly writes this a proportionality and identifies the constant of proportionality. Question 4Select one: a. U ∝ x with constant of proportionality 12 kx . b. U ∝ x2 with constant of proportionality 12 k . c. U ∝ 12 with constant of proportionality kx2 . d. U ∝ 12 x with constant of proportionality kx . e. U ∝ 12 k with constant of proportionality x2 .
A weight of 2.0 N is hung from a spring. The extension produced is 6.0 cm. The 2.0 N weight is removed and an 8.0 N weight is hung from the spring. The spring does not pass its limit of proportionality.What is the new extension of the spring?
A 25.0 cm tall spring is compressed by 12 mm when a 1.00 kg mass is placed on it.(i) (1 mark)Determine the spring constant of the spring.(ii) (1 mark)Calculate the elastic potential energy stored in the spring.(iii) (1 mark)Where did the energy stored in the spring 'come from'?(iv) (2 marks)The spring is now placed horizontally on a frictionless surface with one end attached to a wall and a 740 g mass attached to the other end. The mass is given a push to set it oscillating. What is the frequency of oscillation?(v) (2 marks)A pendulum is placed above the mass-spring system and the bob oscillates back and forth exactly in time with the mass. How long is the pendulum?
A spring a has a force constant of 423 N/m. If the spring is stretched 4.51 cm from the equilibrium position, then what amount of elastic potential energy is stored in the spring?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.