A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from 0 to 5.85 m/s in 0.712 s. What is the magnitude of the linear impulse experienced by a 70.5 kg passenger in the car during this time?
Impulse = change in momentum
I= m(v-u)
I=70.5 (5.85-0)
I=412.4Ns
To calculate the magnitude of the linear impulse experienced by the passenger, we can use the impulse-momentum theorem, which states that the impulse experienced by an object is equal to the change in momentum of that object.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Therefore, the initial momentum of the passenger is zero since the car is initially stopped, and the final momentum is given by:
Final momentum = mass × final velocity
Using the given values:
Mass of the passenger (m): 70.5 kg
Final velocity (v): 5.85 m/s
Final momentum = 70.5 kg × 5.85 m/s
Next, we need to calculate the change in momentum, which is equal to the final momentum minus the initial momentum:
Change in momentum = Final momentum - Initial momentum
= Final momentum - 0 (since initial momentum is zero)
Change in momentum = Final momentum
Substituting the calculated values:
Change in momentum = 70.5 kg × 5.85 m/s
Finally, the impulse experienced by the passenger during this time is equal to the change in momentum:
Impulse = Change in momentum
= 70.5 kg × 5.85 m/s
Therefore, the magnitude of the linear impulse experienced by the passenger is 413.925 N·s (rounded to three decimal places).
To find the magnitude of the linear impulse experienced by the passenger in the car, we can use the principle of impulse-momentum.
The linear impulse is given by the product of the force applied and the time for which it is applied. Mathematically, impulse (J) = force (F) × time (Δt).
To find the force, we can use Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
The mass of the passenger is given as 70.5 kg. To find the acceleration, we can use the formula:
Acceleration (a) = Change in velocity (Δv) / Time (Δt)
The change in velocity (Δv) can be calculated by subtracting the initial velocity from the final velocity:
Δv = Final velocity (v2) - Initial velocity (v1)
Given that the initial velocity is 0 m/s and the final velocity is 5.85 m/s, we can substitute these values into the equation:
Δv = 5.85 m/s - 0 m/s = 5.85 m/s
Now we can substitute the values of mass and acceleration into the equation for force:
F = m × a
F = 70.5 kg × 5.85 m/s / 0.712 s
With this value of force, we can calculate the impulse by multiplying it by the time (0.712 s):
J = F × Δt
J = 70.5 kg × 5.85 m/s / 0.712 s × 0.712 s
Calculating this expression gives us the magnitude of the linear impulse experienced by the passenger in the car during this time.