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You and your brother argue often about how to safely secure a toddler in a moving car. You insist that special toddler seats are critical in improving the chances of a toddler surviving a crash. Your brother claims that, as long as his wife is buckled in next to him with a seat belt while he drives, she can hold onto their toddler on her lap in a crash. You decide to perform a calculation to try to convince your brother. Consider a hypothetical collision in which the 13 kg toddler and his parents are riding in a car traveling at 37 mi/h relative to the ground. The car strikes a wall, tree, or another car, and is brought to rest in 0.14 as. You wish to demonstrate to your brother the magnitude of the force necessary for his wife to hold onto their child during the collision. What is the magnitude of this force (in N)

Respuesta :

Answer:

Force F = 1535.86 N

the force necessary for his wife to hold onto their child during the collision is 1535.86 N

Explanation:

Given;

Mass of toddler m = 13 kg

Velocity v = 37 mi/h = 37 × 0.44704 m/s = 16.54 m/s

Impulse time t = 0.14 seconds

Using the impulse momentum equation,

Impulse = change in momentum

Ft = m(∆v)

Force F = m(∆v)/t

∆v = 16.54 m/s

F = 13×16.54/0.14

Force F = 1535.86 N

pstnonsonjoku

The force required is 1534 N.

The acceleration of the car is obtained from;

v = u - at

Note that the acceleration is negative because the car is coming to rest. Also, the final velocity is zero because the car came to rest.

We now convert the velocity from mi/h to m/s then the initial velocity becomes 16.5 m/s.

Substituting values;

0 =  16.5 - 0.14a

16.5 = 0.14a

a = 16.5/0.14

a = 118 m/s^2

Now;

F = ma

F = 13 kg ×  118 m/s^2 = 1534 N

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