Skip to main content
Ch. 6 - Applications of Integration
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 6 - Applications of Integration문제 6.7.25b
6장, 문제 6.7.25b

Work done by a spring A spring on a horizontal surface can be stretched and held 0.5 m from its equilibrium position with a force of 50 N.
b. How much work is done in compressing the spring 0.5 m from its equilibrium position?

검증된 단계별 안내
1
Identify the spring constant \( k \) using Hooke's Law, which states that the force \( F \) required to stretch or compress a spring is proportional to the displacement \( x \): \[ F = k \times x \] Given \( F = 50 \) N and \( x = 0.5 \) m, solve for \( k \).
Recall that the work done \( W \) in stretching or compressing a spring from its equilibrium position to a displacement \( x \) is given by the formula for elastic potential energy: \[ W = \frac{1}{2} k x^2 \]
Substitute the value of \( k \) found in step 1 and the displacement \( x = 0.5 \) m into the work formula.
Calculate the expression to find the amount of work done in compressing the spring 0.5 m from its equilibrium position.
Interpret the result as the energy stored in the spring due to compression.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Hooke's Law

Hooke's Law states that the force exerted by a spring is proportional to its displacement from the equilibrium position, expressed as F = kx, where k is the spring constant and x is the displacement. This law helps determine the spring constant from the given force and displacement.
추천 영상:
가이드 코스
05:40
Work Done On A Spring (Hooke's Law)

Spring Constant

The spring constant (k) measures the stiffness of a spring and is calculated by dividing the force applied by the displacement (k = F/x). Knowing k allows us to quantify how much force is needed to stretch or compress the spring by a certain amount.
추천 영상:
가이드 코스
05:40
Work Done On A Spring (Hooke's Law)

Work Done by a Spring

The work done in stretching or compressing a spring is the energy stored in it, calculated by W = (1/2)kx². This formula integrates the variable force over the displacement, reflecting that more work is needed as the spring stretches further.
추천 영상:
가이드 코스
05:40
Work Done On A Spring (Hooke's Law)
관련 실천
교과서 질문

Displacement and distance from velocity Consider the velocity function shown below of an object moving along a line. Assume time is measured in seconds and distance is measured in meters. The areas of four regions bounded by the velocity curve and the t-axis are also given.

b. What is the displacement of the object over the interval [2, 6]? 

60
views
교과서 질문

55–58. Marginal cost Consider the following marginal cost functions.


b. Find the additional cost incurred in dollars when production is increased from 500 units to 550 units.


C′(x)=200−0.05x

57
views
교과서 질문

Winding a chain A 30-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain has a density of 5kg/m.

b. How much work is required to wind the chain onto the cylinder if a 50-kg block is attached to the end of the chain?

39
views
교과서 질문

13–16. Displacement from velocity Consider an object moving along a line with the given velocity v. Assume time t is measured in seconds and velocities have units of m/s.


b. Find the displacement over the given interval. 


v(t) = 50e^−2t on [0, 4]

30
views
교과서 질문

Consider the following curves on the given intervals.  


b. Use a calculator or software to approximate the surface area.


y=cos x, for 0≤x≤π/2; about the x-axis

62
views
교과서 질문

"Determine whether the following statements are true and give an explanation or counterexample.


b. The volume of a hemisphere can be computed using the disk method. "

68
views