• MHB
• WMDhamnekar
In summary: The lowest speed that the child can realistically have is then $v=\sqrt{2gh}=9.00\,m/s$.In summary, the mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path. The swing is suspended 2.00 m above the child’s center of mass. The child exerts a force of 905 N on the seat, which is about 4 times the force of gravity. The child can only realistically go as fast as 9.00 m/s at the lowest point of his path.
WMDhamnekar
MHB
Hi,

A mother pushes her child on a swing so that his speed is 9.00 m/s at the lowest point of his path. The swing is suspended 2.00 m above the child’s center of mass.

(a) What is the magnitude of the centripetal acceleration of the child at the low point?

(b) What is the magnitude of the force the child exerts on the seat if his mass is 18.0 kg?

(c) What is unreasonable about these results?

(d) Which premises are unreasonable or inconsistent?

Answer:- (a) $\frac{(9.00 m/s)^2}{2.00 m}=40.5 m/s^2$

(b) Answer given is 905 N. But my answer is $40.5 m/s^2 \times 18.00kg =729 N$ What is wrong with my answer?

How would you answer question (c) and (d)?

Dhamnekar Winod said:
Answer:- (a) $\frac{(9.00 m/s)^2}{2.00 m}=40.5 m/s^2$

(b) Answer given is 905 N. But my answer is $40.5 m/s^2 \times 18.00kg =729 N$ What is wrong with my answer?

There are two forces acting on the child: the normal force from the swing, and the gravitational force.
They are opposite and they must add up to the centripetal force.
In other words, you still need to add the gravitational force.

How would you answer question (c) and (d)?

The acceleration $40.5\,m/s^2$ is about 4 times the acceleration due to gravity. Add gravity itself and we have 5 times. That seems like a lot to subject a child to.
The maximum speed that the child can realistically have, is if we bring the swing up all the way to the side and 2.00 meters up, and then let it swing down.
What will the speed of the child then be at the lowest point?

Hi,
How to compute the maximum speed that the child can realistically have at the lowest point of his path??

Dhamnekar Winod said:
Hi,
How to compute the maximum speed that the child can realistically have at the lowest point of his path??
Easiest is to apply conservation of energy.
The added gravitational energy is $mgh$ with $h=2.00\,m$, which must be equal to the kinetic energy $\frac 12 m v^2$ at the lowest point (disregarding friction).
That is:
$$mgh = \frac 12 mv^2\implies v=\sqrt{2gh}$$

Last edited:

## 1. What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and its magnitude is given by the equation a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

## 2. How is centripetal acceleration different from normal acceleration?

Normal acceleration is the acceleration experienced by an object due to a change in its speed or direction. Centripetal acceleration, on the other hand, is the acceleration experienced by an object moving in a circular path due to the change in its direction.

## 3. What are some real-life examples of centripetal acceleration?

Some examples of centripetal acceleration in everyday life include the motion of a car around a curve, the rotation of a carousel, and the orbit of planets around the sun.

## 4. How is centripetal acceleration related to centripetal force?

Centripetal acceleration and centripetal force are directly related. Centripetal force is the force that causes an object to move in a circular path, and its magnitude is given by the equation F = mv^2/r, where m is the mass of the object. This force is necessary to maintain the centripetal acceleration of the object.

## 5. Can centripetal acceleration be negative?

No, centripetal acceleration cannot be negative. It is always directed towards the center of the circle and its magnitude is always positive. A negative acceleration would mean that the object is moving in the opposite direction, which is not possible in a circular path.

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