suppose that a seat-belted mother riding in an automobile holds a 10 kg baby in her arms. the automobile crashes and decelerates from 50km/h to 0 in .1 s. what average force would the mother have to exert on the baby to hold it?? do you think she can do this?
To determine the average force the mother would have to exert on the baby, we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a), or F = ma.
First, we need to convert the initial velocity of the automobile from km/h to m/s. Since 1 km/h equals 0.2778 m/s, the initial velocity is 50 km/h × 0.2778 m/s = 13.89 m/s.
Next, we need to calculate the acceleration of the automobile using the formula acceleration (a) equals change in velocity (Δv) divided by time (t), or a = Δv / t.
The change in velocity is the difference between the initial velocity and final velocity, which is 0 m/s - 13.89 m/s = -13.89 m/s (negative sign indicates deceleration).
Substituting the values into the formula, we get a = -13.89 m/s / 0.1 s = -138.9 m/s^2.
Now, let's calculate the net force acting on the baby. Since the baby is held by the mother, the only force acting on the baby is the force exerted by the mother. Thus, the net force exerted by the mother on the baby is equal to the mass of the baby multiplied by the acceleration experienced by the baby.
Using F = ma, where the mass (m) is 10 kg and the acceleration (a) is -138.9 m/s^2, we find F = 10 kg × (-138.9 m/s^2) = -1389 N.
The negative sign indicates that the force exerted by the mother is in the opposite direction of the deceleration (opposite to the direction of motion).
Now, let's discuss whether the mother can exert this force. The force of -1389 N is quite large, and it is practically impossible for a person to exert this force on their own. Moreover, in the event of a crash, the force exerted on the baby will be significantly higher due to other factors like airbags, impact forces, and contact with car interiors.
Therefore, it is essential for both the mother and baby to be properly restrained by seat belts and child car seats, respectively, to ensure their safety during a crash.