- #1

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**Problem Statement**

What is the chance of a light car safely rounding an unbanked frictionless curve compared to a heavy car? Both cars have the same speed and tires.

**Solution**

I know that tan(theta)=v^2/(rg) proves that weight does not matter but I do not understand why and my book doesn't explain it very well. Can some one try explaining this concept to me?

2.

**Problem Statement**

A rigid massless rod is rotated about one end in a horizontal circle. There is a mass m_1 attached to the center of the rod and a mass m_2 attached to the outer end of the rod. The inner section of the rod sustains three times as much tension as the outer section. Find the ratio m_2/m_1

**Solution**

Doing a force balance at both m_1 and m_2 shows that the centripetal force (F_c=m*v^2/r) will equal the tension. Though since their velocities will not be the same but their angular velocities will be I replaced velocity with radius*angular velocity.

F_c=m(rw)^2/r

For m_1...

3T=m_1*(rw)^2/r

Solve for T, T=m_1*(rw)^2/(3r)

For m_2...

T=m_2*(2rw)^2/(2r)

Since T=T...

m_1*(rw)^2/(3r)=m_2*(2rw)^2/(2r)

Solving for m_2/m_1 I get 2/3 but my book says the answer is 1/4. Am I wrong or is the book?