The table shows values of a force function f(æ) where a is measured in meters and f(x) in newtons. Use Simpson's Rule to estimate the work done (in joules) by the force in moving an object a distance of 18 meters, giving your answer correct to the nearest whole number. x (m) f(x) (N) 9.8 9.1 8.5 8.0 7.7 7.5 7.4 3 6 12 15 18
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- The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpsons rule to estimate the work done by the force in moving an object a distance of 18 m Answer in joules:The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpson's Rule to estimate the work done by the force in moving an object a distance of 18 m. joules x 0 3 6 9 12 15 18 f(x) 9.9 9.4 8.6 8.1 7.8 7.5 7.3decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem . If false,provide an example,illustration,or briefexplanation of why the statement is false. Q.) The impulse of a force F(t) acting on an object is obtained by integrating F(t) over all values of t.
- Assume that a spring does not follow Hooke’s Law. Instead, the force required to stretch the spring x m from its natural length is F(x) = ksqrt(5 + x2) N. a. If a 3-N force stretches the spring 2 m, find the value of k. b. How much work is required to stretch the spring 1 m from its natural lengthA moonshiner makes the error of filling a glass jar to the brim and capping it tightly. The moonshine expands more than the glass when it warms up, in such a way that the volume increases by 0.2% (that is, ΔV/V0 = 2 ✕ 10-3) relative to the space available. Calculate the force exerted by the moonshine per square centimeter if the bulk modulus is 1.5 ✕ 109 N/m2, assuming the jar does not break. N/cm2A trough with a trapezoidal cross-section, as shown in the figure, contains vegetable oil with density 930 kg/m3. (Use g = 9.8 m/s2 for the acceleration due to gravity.) [I have answer to part a, I just need help with part b] (a) Find the hydrostatic force (in N) on one end of the trough if it is completely full of oil. 54684=N (b)Compute the force (in N) on one end if the trough is filled to a depth of 1.5 m. (Round your answer to two decimal places.) ?=N
- Use Hooke’s Law,which states that the distance a spring stretches or compresses from its natural, or equilibrium, length varies directly as the applied force on the spring.A force of 220 newtons stretches a spring 0.12 meter.What force stretches the spring 0.16 meter?Use Hooke’s Law to determine the work done by the variable force in the spring problem. Six joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.25 meter.Use the concept of Particular Antiderivatives and Rectilinear Motion to answer the problem below: On the edge of an 8m building, Sam throws his toy vertically upwards at initial velocity = 28 m/s. If the only force that acts on the toy is accelerationdue to gravity (-32 ft/s), a. How many seconds will it take for the toy to reach its maximum height?b. What is the toy's speed when it hits the ground?
- Using differentials, determine the approximate increase in the surface area of a sphere if the radius increases from 4cm to 4.05 cm. a. 206.12 cm2 b. 1.26 cm2 c. 100.53 cm2 d. 5.03 cm2Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The antiderivative of f(x) is uniqueHow do you define and calculate the work done by a variable force directed along a portion of the x-axis? How do you calculate the work it takes to pump a liquid from a tank? Give examples.