A man swings his child in a circle of radius 0.75 m .If the mass of child is 25 kg and the child makes one revolution in 1.5 s,what are the magnitude and direction of the force that must be exerted by the man on the child?*assume that the child to be a point particle
Vertical force component = M*g
Radial force component = M V^2/R
V = 2*pi*R/(1.5 s)= 3.142 m/s
R = 0.75 m
M = 25 kg
Do the numbers and compute the magnitude.
To find the magnitude and direction of the force exerted by the man on the child, we need to consider the centripetal force acting on the child as it moves in a circular path.
The centripetal force is given by the formula:
F = m * ω^2 * r
Where:
F = Centripetal force
m = Mass of the child
ω = Angular velocity (2π / T, where T is the time taken for one revolution)
r = Radius of the circular path
Given:
m = 25 kg
r = 0.75 m
T = 1.5 s
First, we need to calculate the angular velocity:
ω = 2π / T
= 2π / 1.5
= 4.1888 rad/s (rounded to four decimal places)
Now, we can calculate the centripetal force:
F = m * ω^2 * r
= 25 * (4.1888)^2 * 0.75
= 256.2475 N (rounded to four decimal places)
Therefore, the magnitude of the force exerted by the man on the child is 256.2475 N.
Since the centripetal force is directed towards the center of the circular path, the force exerted by the man on the child is also directed towards the center of the circle. Thus, the direction of the force is towards the center of the circular path.
To find the magnitude and direction of the force exerted by the man on the child, we need to use the centripetal force formula.
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the child (25 kg)
v is the velocity of the child
r is the radius of the circle (0.75 m)
To find the velocity of the child, we need to convert one revolution in 1.5 seconds to angular velocity. Since one revolution is equal to 2π radians, the angular velocity can be calculated as:
ω = (2π) / T
Where:
ω is the angular velocity
T is the time period for one revolution (1.5 s)
Substituting the values into the equation:
ω = (2π) / 1.5 = 4.19 radians/second
Now, to find the linear velocity (v) of the child, we can use the formula:
v = r * ω
Substituting the values into the equation:
v = 0.75 m * 4.19 rad/s = 3.14 m/s
Now, we can substitute the values of mass (m = 25 kg) and velocity (v = 3.14 m/s) into the centripetal force formula to find the magnitude of the force:
F = (m * v^2) / r
F = (25 kg * (3.14 m/s)^2) / 0.75 m
F = 329.9 N
Therefore, the magnitude of the force exerted by the man on the child is approximately 329.9 Newtons.
To determine the direction of the force, we know that the centripetal force acts towards the center of the circle. In this case, the center of the circle is where the man is holding the child. Thus, the direction of the force is towards the man holding the child.
Therefore, the magnitude of the force is approximately 329.9 N and the direction is towards the man.