As shown in the figure below, a box of mass m = 13.6 kg is released from rest (a

Question

As shown in the figure below, a box of mass m = 13.6 kg is released from rest (at position A) at the top of a 30.0 degree frictionless incline. The box slides a distance d = 3.10 m down the incline before it encounters (at position B) a spring and compresses it an amount x_c = 0.200 m (to point C) before coming momentarily to rest. Using energy content, determine the following. speed of the box at position B V_B = How does the total energy of the box at point A compare to the total energy at point B? What level did you choose for zero gravitational potential energy? Can you write an expression for the gravitational potential energy of an object in terms of Its mass, distance above or below the zero gravitational potential energy level, and the magnitude of the acceleration due to gravity? Can you write an expression for the kinetic energy of an object in terms of its mass and speed? Knowing the potential and kinetic energy of an object, can you determine the total energy of the object? m/s spring constant K = How does the total energy of the box at point A compare to the total energy of the box at point B and then at point C? What position did you choose for zero elastic potential energy of the spring? Can you write an expression for the gravitational potential energy of the box at any position on the incline and the spring potential energy for any compression of the spring? N/m the physical quantity that is constant throughout the process kinetic energy elastic potential energy gravitational potential energy total energy

Explanation / Answer

a) Change in gravitational potential energy = change in kinetic energy

mg d sin 30 degree = 0.5 mv^2

eliminating m on both sides

9.8 x 3.1 x 0.5 = 0.5 x v^2

v = sqrt ( 9.8 x 3.1) = 5.51 m/s

b) decrease in gravitational potential energy tillpoint C = increase in spring P.E.

mg (d+Xc) sin 30 degree = 0.5 k Xc^2

13.6*9.8 (3.1+0.2) *0.5 = 0.5* k * 0.2^2

k = 13.6*9.8* (3.3) /(0.2*0.2) = 10995.6 N/m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.