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
duplicate post; already answered
To find the magnitude and direction of the force exerted by the man on the child, we can start by analyzing the motion of the child.
1. Calculate the angular velocity (ω):
- The child makes one revolution in 1.5 seconds, which means it completes a full circle in that time.
- One revolution is equivalent to 2π radians.
- Therefore, the angular velocity (ω) can be calculated as ω = (2π rad) / (1.5 s).
2. Calculate the linear velocity (v):
- The linear velocity (v) of the child can be calculated using the formula v = ω * r, where r is the radius of the circle.
- In this case, the radius (r) is given as 0.75 m.
v = (2π rad) / (1.5 s) * 0.75 m
v ≈ 3.14 m/s
3. Calculate the centripetal force (F):
- The centripetal force (F) exerted on a moving object in a circular path can be calculated using the formula F = m * a, where m is the mass of the object and a is the acceleration.
- In this case, the centripetal force is provided by the tension in the string, which is the force exerted by the man.
- The acceleration a can be calculated using the formula a = v^2 / r, where v is the linear velocity and r is the radius.
a = (3.14 m/s)^2 / 0.75 m
a ≈ 13.2 m/s²
F = m * a
F = 25 kg * 13.2 m/s²
F ≈ 330 N
4. Determine the direction of the force:
- The force exerted by the man is directed towards the center of the circular motion, which is the inward direction.
- This is because the force required to keep an object in circular motion acts towards the center of the circle.
Therefore, the magnitude of the force exerted by the man on the child is approximately 330 Newtons, and it is directed inward towards the center of the circular motion.
To find the magnitude and direction of the force exerted by the man on the child, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the child's acceleration. We can use the equation for centripetal acceleration:
a = (v^2) / r
where "a" is the acceleration, "v" is the velocity, and "r" is the radius.
The child's velocity can be calculated using the formula:
v = (2 * π * r) / T
where "v" is the velocity, "r" is the radius, and "T" is the time for one complete revolution.
Plugging in the values:
v = (2 * π * 0.75m) / 1.5s
≈ 3.14 m/s
Next, we can calculate the acceleration:
a = (3.14 m/s)^2 / 0.75m
≈ 13.15 m/s^2
Now that we have the acceleration, we can find the force using Newton's second law:
F = m * a
where "F" is the force, "m" is the mass, and "a" is the acceleration.
Plugging in the values:
F = 25 kg * 13.15 m/s^2
≈ 328.75 N
So, the magnitude of the force exerted by the man on the child is approximately 328.75 N.
Now, let's determine the direction of the force. The force exerted by the man on the child is directed towards the center of the circular motion. This force is commonly referred to as the centripetal force. In this case, the centripetal force is directed towards the man.
Therefore, the direction of the force is towards the center of the circle.