Final answer:
To calculate the force exerted by a seatbelt on a passenger during a crash, deceleration is found using the change in velocity over time, and then force is calculated by multiplying the passenger's mass by deceleration according to Newton's second law.
Step-by-step explanation:
Calculating the Force Exerted by a Seat Belt
To calculate the force the seat belt exerts on a passenger during the crash, first, we need to determine the deceleration of the passenger using the formula: deceleration = (final velocity - initial velocity) / time. In this case, the final velocity is 0 m/s (since the car stops), and the initial velocity is 10 m/s (the speed of the car before the crash). The time is given as 0.26 s.
Deceleration = (0 m/s - 10 m/s) / 0.26 s = -38.46 m/s2 (The negative sign indicates a decrease in speed).
Next, we can use Newton's second law to find the force: Force = mass × deceleration. The mass of the passenger is given as 70 kg.
Force = 70 kg × (-38.46 m/s2) = -2692.2 N. The negative sign indicates that the force is in the opposite direction of the motion.
The force the seatbelt exerts on the passenger is therefore 2692.2 N in a direction opposite to the original motion of the car.