A 68 kg runner exerts a force of 59 N. what is the acceleration of the runner
2 answers:
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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.
First of all, we can find the mass of the person, since we know his weight W:
And so
We know for Newton's second law that the resultant of the forces acting on the person must be equal to the product between the mass and the acceleration a of the person itself:
There are only two forces acting on the person: his weight W (downward) and the vincular reaction Rv of the floor against the body (upward). So we can rewrite the previous equation as
We know the acceleration of the system,
(upward, so with same sign of Rv), so we can solve to find the value of Rv, the normal force exerted by the elevator's floor on the person:
And so
We know for Newton's second law that the resultant of the forces acting on the person must be equal to the product between the mass and the acceleration a of the person itself:
There are only two forces acting on the person: his weight W (downward) and the vincular reaction Rv of the floor against the body (upward). So we can rewrite the previous equation as
We know the acceleration of the system,