Respuesta :
Answer:
7 ms⁻¹
Explanation:
When the weight is 50% more, if the actual weight is W, the weight at the dip will be 1.5 Mg . At the bottom, the forces acting are
Weight Mg , vertically downwards
Centripetal force towards the center of the circle
and the normal force N = 1.5 Mg, that acts towards the center
N - Mg = Mv²÷ r
1.5 Mg - Mg = M v² ÷ r
0.5 g = v² ÷ 10
⇒ v = 7 ms⁻¹ Car's speed at the bottom of the dip.
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
We are told that the passengers in the car feel 50% heavier than their true weight as the car goes up. This means that;
F_seat = mg + 0.5mg
F_seat = 1.5mg
Thus;
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 × 9.8 × 10
v² = 49
v = √49
v = 7 m/s
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