The passengers in a roller coaster car feel 50% heavier than their true weight as the car goes through a dip with a 40 m radius

Question

2 years ago

5

of curvature.

1 answer:

inessss [21] · Answer 1 · 2023-12-07T11:34:24+03:00

The speed of the car at the bottom of the dip given the parameters in the equation is; v = 7 m/s

Since the motion is circular, it means that the acceleration of the car will be acting towards the centre of the circle and as a result the acceleration will be acting upwards with the formula; a = v²/r
Now, if the mass of a passenger is denoted as m, then the net force on the passenger will be;

F = mv²/r

Also, in the roller coaster, two other forces are acting which are the force of gravity(F_g) acting downward and also the force of the seat(F_seat) acting upwards. Thus, from equilibrium of forces, we can say that;

F_seat - F_g= mv²/r

Where F_g= mg.

Thus; F_seat - mg mv²/r

1.5mg - mg mv²/r

divide through by m to get; 0.5g = v²/r

Plug in the relevant values;

0.5(9.8) = v²/10

v² = 0.5 x 9.8 × 10

v² = 49

v = 7

The speed of Car is 7 m/s

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