How much force would a 55kg person experience on a roller coaster if they travel through a loop with a radius of 55kg at a speed
of 14.1 m/s?
1 answer:
Answer:
200 N
Explanation:
For a body moving in uniform circular motion, the force acting on it will be <em>centripetal force</em> and its direction is <em>radially inward</em> , pointing to the center.
The radially inward acceleration, or the centripetal acceleration is given by :
a = v² / r
where v is the speed at which the body is moving and r is the radius of the circle
Given-
m = 55kg
v = 14.1 m/s
r= 55m
We know that F = ma
⇒ F = m ( v²/ r )
⇒ F = 55 x 14.1 x 14.1 / 55
⇒ F =14.1 x 14.1 = 200 N
∴ <em>The force acting is 200 N</em>.
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Answer:
a)η = 69.18 %
b)W= 1210 J
c)P=3967.21 W
Explanation:
Given that
Q₁ = 1749 J
Q₂ = 539 J
From first law of thermodynamics
Q₁ = Q₂ +W
W=Work out put
Q₂=Heat rejected to the cold reservoir
Q₁ =heat absorb by hot reservoir
W= Q₁- Q₂
W= 1210 J
The efficiency given as
η = 69.18 %
We know that rate of work done is known as power
P=3967.21 W
A) 19.6 m/s (downward)
B) 576 J
C) 19.6 m
D) Velocity: not affected, kinetic energy: doubles, distance: not affected
Explanation:
A)
An object in free fall is acted upon one force only, which is the force of gravity.
Therefore, the motion of an object in free fall is a uniformly accelerated motion (constant acceleration). Therefore, we can find its velocity by applying the following suvat equation:
where:
v is the velocity at time t
u is the initial velocity
is the acceleration due to gravity
For the object in this problem, taking downward as positive direction, we have:
(the object starts from rest)
Therefore, the velocity after
t = 2 s
is:
(downward)
B)
The kinetic energy of an object is the energy possessed by the object due to its motion.
It can be calculated using the equation:
where
m is the mass of the object
v is the speed of the object
For the object in the problem, at t = 2 s, we have:
m = 3 kg (mass of the object)
v = 19.6 m/s (speed of the object)
Therefore, its kinetic energy is:
C)
In order to find how far the object has fallen, we can use another suvat equation for uniformly accelerated motion:
where
s is the distance covered
u is the initial velocity
t is the time
a is the acceleration
For the object in free fall in this problem, we have:
u = 0 (it starts from rest)
(acceleration of gravity)
t = 2 s (time)
Therefore, the distance covered is
D)
Here the mass of the object has been doubled, so now it is
M = 6 kg
For part A) (final velocity of the object), we notice that the equation that we use to find the velocity does not depend at all on the mass of the object. This means that the value of the final velocity is not affected.
For part B) (kinetic energy), we notice that the kinetic energy depends on the mass, so in this case this value has changed.
The new kinetic energy is
where
M = 6 kg is the new mass
v = 19.6 m/s is the speed
Substituting,
And we see that this value is twice the value calculated in part A: so, the kinetic energy has doubled.
Finally, for part c) (distance covered), we see that its equation does not depend on the mass, therefore this value is not affected.