A roller coaster cart at position A has a velocity of 10 m/s and a height of 5 m

Question

A roller coaster cart at position A has a velocity of 10 m/s and a height of 5 meters. Answer the following: a. What is the cart's velocity at position B, if there is no height at position B? b. What is the cart's velocity at position C if the height is 25 meters? c. Does the mass of the cart affect its velocity at any point along the track? Explain: A solid sphere with a mass of 10 kg and a radius of 0.2 meters is initially at rest at the top of a hill, a height of 5 meters above the ground. The ball begins to roll down the hill, gain speed along the way. Answer the following: a. What type(s) of energy does the ball have at the top of the hill? b. What type(s) of energy does the ball have when it is half way down the hill? c. What type(s) of energy does the ball have at the bottom of the hill? d. What is the potential energy of the ball at the top of the hill? e. What is the linear velocity of the ball at the bottom of the hill? f. What is the angular velocity of the ball at the bottom of the hill?

Explanation / Answer

(1)a) using the conservation of energy at A and B

KEa + PEa= KEb+ PEb

1/2 mVa2+ m g Ha=1/2 mVb2+ m g Hb

mass m cancels on both sides

1/2 (10)2 +(9.8)(5)=1/2 Vb2+ 9.8 (0)

Vb= 14.07 m/s.

(b)using the conservation of energy at B and C

KEb + PEb= KEc+ PEc

1/2 mVb2+ m g Hb=1/2 mVc2+ m g Hc

mass m cancels on both sides

1/2 (14.07)2 +(9.8)(0)=1/2 Vc2+ 9.8 (25)

Vc2=-292 which is not possible as v will be a complex number

so we can say that the roller coaster doesnot each the point C

(c) when we use the equation for conservation of energy , the mass cancels on both sides. so mass has no effect on the velocity at any point along the track..

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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