5. A woman is wearing her seat belt while driving 95km/h. She finds it necessary to slam on her brakes, and she slows uniformly to a stop in 5 s. Calculate the average force exerted on her by the seat belt (neglecting friction with the seat)? Express the result as a multiple of the woman’s weight
To calculate the average force exerted on the woman by the seat belt, we can use Newton's second law of motion, which states that the force is equal to the mass of an object multiplied by its acceleration:
F = m * a
In this case, the woman's acceleration can be calculated using the equation for uniformly decelerated motion:
a = (v_f - v_i) / t
where:
v_f = final velocity (0 m/s, since she comes to a stop)
v_i = initial velocity (95 km/h converted to m/s)
t = time taken to decelerate (5 s)
So, let's calculate the initial velocity (v_i):
v_i = 95 km/h * (1000 m/1 km) * (1 h/3600 s) = 26.39 m/s
Now we can calculate the acceleration (a):
a = (0 m/s - 26.39 m/s) / 5 s = -5.28 m/s^2
The negative sign indicates that it is a deceleration.
Next, we need to calculate the mass of the woman, but it is not provided in the question. Let's assume a mass of 60 kg.
Now we can substitute the values into the formula F = m * a:
F = 60 kg * (-5.28 m/s^2) = -316.8 N
The negative sign tells us that the force exerted by the seat belt is in the opposite direction of motion. To express the result as a multiple of the woman's weight, we need to divide the force by her weight.
To calculate the woman's weight, we can use the formula for weight:
Weight = mass * acceleration due to gravity
Let's assume the acceleration due to gravity as 9.8 m/s^2.
Weight = 60 kg * 9.8 m/s^2 = 588 N
Finally, we can express the average force as a multiple of the woman's weight:
Force / Weight = (-316.8 N) / 588 N = -0.539
Therefore, the average force exerted on the woman by the seat belt is approximately -0.539 times her weight. The negative sign implies that the force is in the opposite direction of her weight.