Question

A 1.20 kg water balloon will break if it experiences more than 530 N of force. Your 'friend' whips the water balloon toward you at 13.0 m/s. The maximum force you apply in catching the water balloon is twice the average force. How long must the interaction time of your catch be to make sure the water balloon doesn't soak you

Answer 1

To catch the water balloon without it breaking, you need to apply a force that does not exceed 530 N. You must catch the balloon with a maximum force that is twice the average force. Using Newton's second law and the given information, you can calculate the time required to catch the balloon without it breaking.

Step-by-step explanation:

To prevent the water balloon from breaking, you need to catch it with a force that does not exceed 530 N. According to the question, the maximum force you apply in catching the water balloon is twice the average force.

Let's assume the average force you apply is x N. So, the maximum force you can apply is 2x N. To calculate the time required to catch the balloon, we need to use Newton's second law, which states that force (F) is equal to mass (m) multiplied by acceleration (a).

The water balloon has a mass of 1.20 kg and a velocity (v) of 13.0 m/s. When catching the balloon, it comes to a stop, so the final velocity (vf) is 0 m/s. Therefore, the acceleration (a) can be calculated using the equation a = (vf - vi) / t, where vi is the initial velocity and t is the time. Rearranging the equation gives t = (vf - vi) / a.

Since the maximum force you can apply is 2x N, the acceleration can be calculated using the equation F = ma, where F is the force, m is the mass, and a is the acceleration. Rearranging the equation gives a = F / m. Substituting 2x for F and 1.20 kg for m, we get a = 2x / 1.20 kg.

Now, we can substitute the values into the equation t = (vf - vi) / a to calculate the time required to catch the balloon without it breaking. Rearranging the equation gives t = (0 - 13.0 m/s) / (2x / 1.20 kg).

Answer 2

t = 0.029s

Step-by-step explanation:

In order to calculate the interaction time at the moment of catching the ball, you take into account that the force exerted on an object is also given by the change, on time, of its linear momentum:

`F=(\Delta p)/(\Delta t)=m(\Delta v)/(\Delta t)` (1)

m: mass of the water balloon = 1.20kg

Δv: change in the speed of the balloon = v2 - v1

v2: final speed = 0m/s (the balloon stops in my hands)

v1: initial speed = 13.0m/s

Δt: interaction time = ?

The water balloon brakes if the force is more than 530N. You solve the equation (1) for Δt and replace the values of the other parameters:

`|F|=|530N|= |m(v_2-v_1)/(\Delta t)|\\\\|530N|=| (1.20kg)(0m/s-13.0m/s)/(\Delta t)|\\\\\Delta t=0.029s`

The interaction time to avoid that the water balloon breaks is 0.029s