From the second law of motion and the equation for velocity EF ΣΕ = ma v² = + 2a(x2-11) Derive the Work - Energy equation: W = K₂-K₁
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- A box of mass 'm' is pushed into a spring with spring constant 'k'. The spring is displaced a total length of Δx, and then we let go of the box. From the work-energy theorem, what is the final velocity of the box after we let go?Time yourself while running up a flight of steps, and compute the average rate at which you do work against the force of gravity. Express your answer in watts and in horsepower.A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop). c)What is the child's final speed, vf in m/s?
- In a time of T seconds, a motorcycle can accelerate from rest to the speed v. (a) Determine the amount of time (in terms of 7) required for it to accelerate from v to 6v if the power output remains constant. At = (b) Determine the speed of the motorcycle (in terms of v) 3T after starting. Vf=A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop). What is the child's final speed, vf in m/s?What is the efficiency of an out-of-condition professor who does 1.90 ✕ 105 J of useful work while metabolizing 510 kcal of food energy? (Enter your answer as a percentage. Enter a number.)% How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 25%? (Enter a number.)kcal
- Force = 4x ^ 4 - 3x. Find the work in mks units done by the force for a distance of x = 1 to x = 7:SQU is trying a new particle accelerator design with a mechanical component using a spring that does not obey Hooke's law. When stretched/compressed x metres, it exerts a force of 39.6x+51.6x2 (a) Compute the work required to stretch the spring from x= 1.0 m to x 1.3 m.Two constant forces F1 = 5 ^i +4.7 j+7.3^ k N and F2 = 3.6^i -4.4 j-2.3^k N act together on an object causes a displacement from position r1 = 3.7^i+ 4 j+8.9° k cm to position r2= 9.1°i + 2.1 `j+ 5.7^k cm. Determine the total work done (J) on the object. Answer:
- Problem 2: A certain spring has a spring constant k₁ = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant then changes to k₂ = 250 N/m as the spring is stretched to x2= 65 cm. From x₂= 65 cm to x3 = 89 cm the spring force is constant at F3 = 105 N.(a) What is the efficiency of an out-of-condition professor who does 2.00 × 105 J of useful work while metabolizing 510 kcal of food energy? (Enter your answer as a percentage. Enter a number.) % (b) How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 20%? (Enter a number.) kcal(a) What is the efficiency of an out-of-condition professor who does 2.30 × 105 J of useful work while metabolizing 490 kcal of food energy? (Enter your answer as a percentage. Enter a number.) % (b) How many food calories (in kcal) would a well-conditioned athlete metabolize in doing the same work with an efficiency of 25%? (Enter a number.) kcal