A capsule of mass m falls from rest through a tunnel that connects Earths south

Question

A capsule of mass m falls from rest through a tunnel that connects Earths south and north poles as shown in the figure here. Consider the moment when the capsule is at distance r from Earth's center for the questions below. Assume Earth has the same constant density inside Earth (a) Calculate the work done by the gravitational force by Earth to move the capsule from the surface of Earth to its center. (b) Get the formula for the gravitational potential energy as a function of r. Specify where you have the reference point and explain why.

Explanation / Answer

Work done is W = Force F*dispalcement S

W = F*S*cos(theta)

theta is the angle between Force and disalcement

here theta = 0 degrees

W = F*S = m*g*r = mgr

b) Since only conservative force ( gravotational force ) is acting on the mass,then work done is W = (U1-U2) = m*g*r - 0 = m*g*r is the answer for b) ,reference point is the center of teh earth

U1 is the potential energy at a distance r from center of earth

U2 is the potential energy at center of earth = m*g*r = m*g*0 = 0

So U1 = W = m*g*r

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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