Question

In the figure below a frictionless roller coaster car of mass m = 825 kg tops the first hill with speed v0=17.0 m/s at height h=42.0 m. (a) How much work does the gravitational force do on the car from that point to point A on the next hill (note that both hilltops are at the same height)? (b) How much work does the force of gravity do to point B on the following hill? (c) And what about from point A to point C in the following trough? (d) What is the value of the gravitational potential energy at A and at B? (e) If the mass of the car were doubled, would the change in gravitational potential energy of the system between points A and B increase, decrease or remain the same? Project You are planning out a roller coaster for a client. We want the experience to be such that on the first two hills the speed of the car at the top is (almost) zero (h=42.0 m). However, we want the passenger to be weightless when he/she is on hill B. Looking at the figure above, determine (a) What velocity do we need to impact to the car so that it reaches the first hill with zero velocity. (b) Given that the car just manages to move past the first peak, what velocity would it have on the second hill (marked A in the figure) if there were no friction? (c) If the third hill (called B) could be considered to be a circular arch with a radius of curvature r = 10 m. How high should the height of hill B be so that the passenger is weightless there?

          In the figure below a frictionless roller coaster car of mass m = 825 kg tops the first hill with speed v0=17.0 m/s at height h=42.0 m.

(a) How much work does the gravitational force do on the car from that point to point A on the next hill (note that both hilltops are at the same height)?

(b) How much work does the force of gravity do to point B on the following hill?

(c) And what about from point A to point C in the following trough?

(d) What is the value of the gravitational potential energy at A and at B?

(e) If the mass of the car were doubled, would the change in gravitational potential energy of the system between points A and B increase, decrease or remain the same?

Project

You are planning out a roller coaster for a client. We want the experience to be such that on the first two hills the speed of the car at the top is (almost) zero (h=42.0 m). However, we want the passenger to be weightless when he/she is on hill B. Looking at the figure above, determine

(a) What velocity do we need to impact to the car so that it reaches the first hill with zero velocity.
(b) Given that the car just manages to move past the first peak, what velocity would it have on the second hill (marked A in the figure) if there were no friction?
(c) If the third hill (called B) could be considered to be a circular arch with a radius of curvature r = 10 m. How high should the height of hill B be so that the passenger is weightless there?

In the figure below a frictionless roller coaster car of mass m = 825 kg tops the first hill with speed v0=17.0 m/s at height h=42.0 m.

(a) How much work does the gravitational force do on the car from that point to point A on the next hill (note that both hilltops are at the same height)?

(b) How much work does the force of gravity do to point B on the following hill?

(c) And what about from point A to point C in the following trough?

(d) What is the value of the gravitational potential energy at A and at B?

(e) If the mass of the car were doubled, would the change in gravitational potential energy of the system between points A and B increase, decrease or remain the same?

Project

You are planning out a roller coaster for a client. We want the experience to be such that on the first two hills the speed of the car at the top is (almost) zero (h=42.0 m). However, we want the passenger to be weightless when he/she is on hill B. Looking at the figure above, determine

(a) What velocity do we need to impact to the car so that it reaches the first hill with zero velocity.
(b) Given that the car just manages to move past the first peak, what velocity would it have on the second hill (marked A in the figure) if there were no friction?
(c) If the third hill (called B) could be considered to be a circular arch with a radius of curvature r = 10 m. How high should the height of hill B be so that the passenger is weightless there?

Added by Martin V.

Question

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