- #1

altecsonyc

Can Someone please help me with this problem! I need some hints how to solve this problem, i am already stuck on part A :(.

This is my practice assignment for the final coming up next 2 weeks. Unfortunately, the professor does not provide solution.

THE PICTURE OF THIS PROBLEM IS ILLUSTRATED BY THE LINK BELOW.

Starting from the initial position (the origin of the coordinate system) a cart with a mass of 2000 kg is accelerated from the initial velocity zero by acceleration a1 which is uniform over a segment of 40 m. Following this segment, the cart proceeds through a turn (20 m radius), is then accelerated again over a segment of 10 m length, coasts toward the top of a hill where its velocity is near zero. The cart then rolls down to ground level, through a circular valley (radius 10 m) and along a straight segment of 2 m length, before leaving the track in free fight, initially inclined at 45 degree. In order to ensure a safe landing, an angular impulse is exerted on the cart just before leaving the track, causing the cart to rotate by a constant angular velocity w, during the flight. This rotation is necessary to have the cart axis aligned with the track at the landing point. Departure and landing occur at the same vertical position. On a short segment of 5 m the cart is decelerated by a3, before coasting through the second turn (20 m radius) and it is further decelerated uniformly (a4) over the final 30 m to come to a full stop at the origin of the coordinate system.

Determine the following design parameters:

a) Appropriate accelerations a1, a2, to meet the following requirements:

_ The cart must come to a stop on top of the hill.

_ The magnitude of the acceleration through the first turn must not be larger than 3g.

b) The coordinates of the point where the cart departs into free flight.

c) The velocity of the cart at the point of departure.

d) The coordinates of the landing point and the flight path angle (_2) at that point.

e) The duration of the flight, and the angular velocity w which is required to have the cart aligned with the track at landing.

f) The velocity of the cart as it reaches ground level (just before the 5m deceleration segment).

g) Appropriate accelerations a3, a4, to meet the following requirements:

_ The cart must come to a full stop at the origin of the coordinate system.

_ The magnitude of the acceleration through the second turn must not be larger than 3g.

h) The duration of the entire ride.

*PS. This problem will help you with the final. GOOD LUCK!

http://img355.imageshack.us/img355/11/pic2jf.jpg [Broken]

This is my practice assignment for the final coming up next 2 weeks. Unfortunately, the professor does not provide solution.

THE PICTURE OF THIS PROBLEM IS ILLUSTRATED BY THE LINK BELOW.

Starting from the initial position (the origin of the coordinate system) a cart with a mass of 2000 kg is accelerated from the initial velocity zero by acceleration a1 which is uniform over a segment of 40 m. Following this segment, the cart proceeds through a turn (20 m radius), is then accelerated again over a segment of 10 m length, coasts toward the top of a hill where its velocity is near zero. The cart then rolls down to ground level, through a circular valley (radius 10 m) and along a straight segment of 2 m length, before leaving the track in free fight, initially inclined at 45 degree. In order to ensure a safe landing, an angular impulse is exerted on the cart just before leaving the track, causing the cart to rotate by a constant angular velocity w, during the flight. This rotation is necessary to have the cart axis aligned with the track at the landing point. Departure and landing occur at the same vertical position. On a short segment of 5 m the cart is decelerated by a3, before coasting through the second turn (20 m radius) and it is further decelerated uniformly (a4) over the final 30 m to come to a full stop at the origin of the coordinate system.

Determine the following design parameters:

a) Appropriate accelerations a1, a2, to meet the following requirements:

_ The cart must come to a stop on top of the hill.

_ The magnitude of the acceleration through the first turn must not be larger than 3g.

b) The coordinates of the point where the cart departs into free flight.

c) The velocity of the cart at the point of departure.

d) The coordinates of the landing point and the flight path angle (_2) at that point.

e) The duration of the flight, and the angular velocity w which is required to have the cart aligned with the track at landing.

f) The velocity of the cart as it reaches ground level (just before the 5m deceleration segment).

g) Appropriate accelerations a3, a4, to meet the following requirements:

_ The cart must come to a full stop at the origin of the coordinate system.

_ The magnitude of the acceleration through the second turn must not be larger than 3g.

h) The duration of the entire ride.

*PS. This problem will help you with the final. GOOD LUCK!

http://img355.imageshack.us/img355/11/pic2jf.jpg [Broken]

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