A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing its speed from zero to 5.47m/s in 0.919s. What linear impulse does a 74.1kg passenger in the car experience?
impulse = change in momentum
= 74.1 * 5.47
To find the linear impulse experienced by the passenger, we can use the formula:
Impulse = Change in momentum
The momentum of an object is given by the equation:
Momentum = mass * velocity
First, let's calculate the initial momentum of the car when it is stopped:
Initial momentum = mass * initial velocity
Given:
Mass of the passenger = 74.1 kg
Initial velocity of the car = 0 m/s
Initial momentum = 74.1 kg * 0 m/s = 0 kg·m/s
Next, we'll calculate the final momentum of the car:
Final momentum = mass * final velocity
Given:
Mass of the passenger = 74.1 kg
Final velocity of the car = 5.47 m/s
Final momentum = 74.1 kg * 5.47 m/s = 405.327 kg·m/s
Now, let's calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = 405.327 kg·m/s - 0 kg·m/s = 405.327 kg·m/s
Therefore, the linear impulse experienced by the 74.1 kg passenger in the car is 405.327 kg·m/s.
To calculate the linear impulse experienced by the passenger in the car, we need to use the impulse-momentum principle. The principle states that the change in momentum of an object is equal to the impulse applied to it.
Impulse (J) is the product of the force applied to an object and the time interval during which the force is applied. Mathematically, it is given by the formula:
J = F * Δt
Where:
J = impulse
F = force applied
Δt = time interval
Momentum (p) is the product of an object's mass and its velocity. Mathematically, it is given by the formula:
p = m * v
Where:
p = momentum
m = mass of the object
v = velocity of the object
Given:
Mass of the passenger (m) = 74.1 kg
Change in velocity (Δv) = final velocity (v) - initial velocity (u) = 5.47 m/s - 0 m/s = 5.47 m/s
Time interval (Δt) = 0.919 s
We can calculate the impulse experienced by the passenger by substituting the values into the formula for impulse:
J = F * Δt
J = m * Δv
Rearranging the equation, we can solve for the force (F):
F = J / Δt
F = m * Δv / Δt
Now, substituting the given values:
F = 74.1 kg * 5.47 m/s / 0.919 s
Calculating this expression will give us the force applied to the passenger.