A car moving at 8 m/s crashes into a barrier and stops in 0.050 s. There is a 19-kg child in the car. Assume that the child's velocity is changed by the same amount as that of the car, and in the same time period. (a) What is the impulse needed to stop the child in N*s?(b) What is the average force on the child in N? (c) What is the approximate mass of an object in kg whose weight equals the force in part (b)?
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To solve this problem, we need to use the concepts of impulse and average force.
(a) In order to find the impulse needed to stop the child, we need to use the equation:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = mass * velocity
Since both the car and the child experience the same change in velocity and in the same time period, we can use the equation:
Impulse = Change in momentum = mass * change in velocity
Now let's calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity
Since the car comes to a stop, the final velocity is zero:
Change in velocity = 0 - 8 m/s = -8 m/s
Using this value, let's calculate the impulse:
Impulse = mass * change in velocity
Impulse = 19 kg * (-8 m/s)
Impulse = -152 N*s (Note: The negative sign indicates the direction of the impulse, in this case, opposite to the initial direction of motion.)
So, the impulse needed to stop the child is -152 N*s.
(b) The average force experienced by an object can be calculated using the formula:
Average force = Impulse / Time
Since we have already calculated the impulse, we can use the given time period of 0.050 s:
Average force = -152 N*s / 0.050 s
Average force ≈ -3040 N (Note: The negative sign indicates the direction of the force, in this case, opposite to the initial direction of motion.)
So, the average force on the child is approximately -3040 N.
(c) The weight of an object is given by the formula:
Weight = mass * gravitational acceleration
To find the approximate mass of an object whose weight equals the force in part (b), we can rearrange the formula:
mass = Weight / gravitational acceleration
Assuming the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the mass:
mass = -3040 N / 9.8 m/s^2
mass ≈ -310.2 kg (Note: The negative sign indicates the direction of the force, not the mass itself. Mass cannot be negative.)
So, the approximate mass of an object whose weight equals the force in part (b) is approximately 310.2 kg.