What is the radius of an automobile tire that turns with a period of 0.091 s and has a linear
1 answer:
Answer:
1) The radius of the tire is approximately 0.28966 meters
2) The centripetal force is the force that keeps a body moving on a circular path
Explanation:
1) The linear speed of the automobile tire = 20.0 m/s
The period with which the tire turns = 0.091 s
The period = The time it takes to make a complete turn
Therefore;
The number of turns in 1 second = 1/0.091 ≈ 10.989 turns
The distance covered with 10.989 turns, assuming no friction = 10.989 × The circumference of the tire
∴ The distance covered with 10.989 turns, assuming no friction = 10.989 × 2 × π × Radius of the tire
From the speed of the car, 20.0 m/s, we have;
The distance covered in 1 second = 20.0 meters
Therefore;
10.989 × 2 × π × Radius of the tire = 20.0 meters
Radius of the tire = (20.0 meters)/(10.289 × 2 × π) ≈ 0.28966 meters
The radius of the tire ≈ 0.28966 meters
2) The centripetal force is the force required to maintain the curved motion of an object, and having a direction towards the center of the rotary motion.
The centripetal force is given by the formula,
Where;
F = The centripetal force
m = The mass of the object
v = The linear velocity of the object
r = The radius of the rotational motion.
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Answer:
F = 4000 N
Explanation:
given,
mass of rocket (M)= 5000 Kg
10 Kg gas burns at speed (m)= 4000 m/s
time = 10 s
average force = ?
at the end the rocket is at rest
by conservation of momentum
M v + m v' = 0
5000 x v - 10 x 4000 = 0
5000 v = 40000
v = 8 m/s
speed of rocket = 8 m/s
now,
we know
change in momentum = F x Δ t
F = 4000 N
Hence, the average force applied to the rocket is equal to F = 4000 N
a) The mass is 0.23 kg
b) The spring constant is 1.25 N/m
c) The frequency is 1.42 Hz
d) The speed of the block is 1.08 m/s
Explanation:
a)
We can find the mass of the block by applying the law of conservation of energy: in fact, the total mechanical energy of the system (which is sum of elastic potential energy, PE, and kinetic energy, KE) is constant:
The potential energy is given by
where k is the spring constant and x is the displacement. When the block is crossing the position of equilibrium, x = 0, so all the energy is kinetic energy:
(1)
where
m is the mass of the block
is the maximum speed
We also know that the total energy is
Re-arranging eq.(1), we can find the mass:
b)
The maximum speed in a spring-mass system is also given by
where
k is the spring constant
m is the mass
A is the amplitude
Here we have:
is the maximum speed
m = 0.23 kg is the mass
A = 14.0 cm = 0.14 m is the amplitude
Solving for k, we find the spring constant
c)
The frequency in a spring-mass system is given by
where
k is the spring constant
m is the mass
In this problem, we have:
k = 18.3 N/m is the spring constant (found in part b)
m = 0.23 kg is the mass (found in part a)
Substituting and solving for f, we find the frequency of the system:
d)
We can solve this part by using the law of conservation of energy; in fact, we have
Where v is the speed of the system when the displacement is equal to x.
We know that the total energy of the system is
E = 0.18 J
Also we know that
k = 18.3 N/m is the spring constant
m = 0.23 kg is the mass
Substituting
x = 7.00 cm = 0.07 m
We can solve the equation to find the corresponding speed v:
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