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Svetach [21]
3 years ago
9

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 11-m-hi

gh hill, then descends 19 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.3 m and that a loaded car will have a maximum mass of 410 kg . For safety reasons, the spring constant should be 12 % larger than the minimum needed for the car to just make it over the top. What is the maximum speed of a 340kg car if the spring is compressed the full amount?
Physics
1 answer:
True [87]3 years ago
4 0

Answer:

m = maximum mass of the coaster = 410 kg

d = maximum spring compression = 2.3 m

h = maximum height of the track = 11 m

H = maximum difference in height of the track = 19 m

g = acceleration by gravity = 9.8 m/s²

k = spring constant (without safety margin) = ?

K = spring constant (with safety margin) = ?

V = maximum speed of the coaster = ?

The gravitational potential energy of the coaster on the top of the 11 m high hill (relative to its initial starting point) is:

PEg = m g h

PEg = (410 kg) (9.8 m/s²) (11 m)

PEg = 44198 J

To reach that height, the elastic potential energy stored in the spring must be the same, so:

PEg = PEe = k d² / 2

(44198 J) = k (2.3 m)² / 2

k = 16710 N/m

Adding 14% to that value, you get:

K = 1.14 (16710 N/m)

K = 19045 N/m - answer spring constant

When fully compressed, the elastic potential energy stored in the spring is:

PEe = K d² / 2

PEe = (19045 N/m) (2.3m)² / 2

PEe = 51326 J

The difference in height between the starting point and the lowest point of the track is:

Δh = H - h

Δh = (19 m) - (11 m)

Δh = 8 m

So the initial gravitational potential energy of 330 kg coaster, relative to the lowest point, is

PEg = m g Δh

PEg = (340 kg) (9.8 m/s) (8 m)

PEg = 26656 J

The total energy of the coaster at its starting point (again, relative to the lowest point) is:

TE = PEe + PEg

TE = (51326J) + (26656 J)

TE = 77982J

At the lowest point of the track, all that energy is converted to kinetic energy, so the speed at that point will be:

TE = KE = m V² / 2

(77982 J) = (340kg) V² / 2

V = 21.46 m/s - answer maximum speed

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in order to qualify for the finals in a racing event, a race car must achieve an average speed of 278 km/h on a track with a tot
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The minimum average speed it must have in the second half of the event in order to qualify is 414.7 km/h.

<h3>What is average speed?</h3>

The average speed of an object is the ratio of total distance traveled by the object to the total time of motion of the object.

<h3>Total time taken by the car during the entire race</h3>

time = distance/average speed

time = (1.41 km) / (278 km/h)

time = 0.0051 hr

The car travels the first half of the race, d (¹/₂ x 1410 m) at 210 km/h;

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t1 = 0.705/210

t1 = 0.0034 hr

<h3>time for the second half</h3>

t2 = 0.0051 - 0.0034 hr

t2 = 0.0017 hr

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v = d/t

v = 0.705 km / 0.0017 hr

v = 414.7 km/hr

Thus, the minimum average speed it must have in the second half of the event in order to qualify is 414.7 km/h.

Learn more about average speed here: brainly.com/question/4931057

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