In a particular crash test, an automobile of
mass 1369 kg collides with a wall and bounces
back off the wall. The x components of the initial and final speeds of the automobile are
10 m/s and 1.9 m/s, respectively.
If the collision lasts for 0.18 s, find the
magnitude of the impulse due to the collision.
Answer in units of kg · m/s
Well, it seems like the car had a bit of a "crash"ing moment! Let's calculate the magnitude of the impulse, shall we?
We can use the formula for impulse, which is given by the change in momentum. The magnitude of impulse (J) is equal to the change in momentum (Δp).
The initial momentum (p_initial) is given by the mass (m) times the initial velocity (v_initial):
p_initial = m * v_initial
The final momentum (p_final) is given by the mass (m) times the final velocity (v_final):
p_final = m * v_final
The change in momentum (Δp) is then given by:
Δp = p_final - p_initial
Now we can plug in the values:
m = 1369 kg
v_initial = 10 m/s
v_final = 1.9 m/s
p_initial = 1369 kg * 10 m/s = 13690 kg·m/s
p_final = 1369 kg * 1.9 m/s = 2605.1 kg·m/s
Δp = p_final - p_initial = 2605.1 kg·m/s - 13690 kg·m/s = -11084.9 kg·m/s
So, the magnitude of the impulse due to the collision is 11084.9 kg·m/s.
To find the magnitude of the impulse during the collision, you can use the impulse-momentum principle which states that the impulse experienced by an object during a collision is equal to the change in momentum of the object.
Impulse = Change in momentum
The momentum of an object can be calculated using the formula:
Momentum = Mass * Velocity
Given:
Mass of the automobile (m) = 1369 kg
Initial x-component velocity (vi) = 10 m/s
Final x-component velocity (vf) = 1.9 m/s
Collision time (t) = 0.18 s
First, calculate the initial momentum (pi) of the automobile:
pi = m * vi
pi = 1369 kg * 10 m/s
Next, calculate the final momentum (pf) of the automobile:
pf = m * vf
pf = 1369 kg * 1.9 m/s
Now, calculate the change in momentum:
Change in momentum = pf - pi
Next, calculate the impulse:
Impulse = Change in momentum = pf - pi
Finally, substitute the values and calculate the magnitude of the impulse:
Impulse = 1369 kg * 1.9 m/s - 1369 kg * 10 m/s
Impulse = (1369 kg * 1.9 m/s) - (1369 kg * 10 m/s)
Impulse = 2605.1 kg * m/s - 13690 kg * m/s
Impulse = -11084.9 kg * m/s
Since impulse is a vector quantity, the magnitude of the impulse is equal to 11084.9 kg * m/s.
Therefore, the magnitude of the impulse due to the collision is 11084.9 kg · m/s.
To find the magnitude of the impulse due to the collision, we can use the principle of impulse-momentum. The impulse is the change in momentum of the automobile, and it can be calculated by multiplying the average force during the collision by the duration of the collision.
First, let's calculate the initial momentum and final momentum of the automobile:
Initial momentum (p₁) = mass (m) * initial velocity (v₁)
Final momentum (p₂) = mass (m) * final velocity (v₂)
Given:
Mass of automobile (m) = 1369 kg
Initial velocity (v₁) = 10 m/s
Final velocity (v₂) = 1.9 m/s
Collision duration (Δt) = 0.18 s
Using the given values, we can calculate the initial and final momenta:
p₁ = m * v₁
p₂ = m * v₂
p₁ = 1369 kg * 10 m/s = 13690 kg·m/s
p₂ = 1369 kg * 1.9 m/s = 2595.1 kg·m/s
The change in momentum, also known as impulse (J), is given by:
J = p₂ - p₁
J = 2595.1 kg·m/s - 13690 kg·m/s
J = -11094.9 kg·m/s (note that the negative sign indicates a change in direction)
To find the magnitude of the impulse, we neglect the negative sign:
Magnitude of impulse = |J| = 11094.9 kg·m/s
Therefore, the magnitude of the impulse due to the collision is 11094.9 kg·m/s.
Divide the momentum change by the tuime interval of contact. (Take care to reverse the sign when the velocity direction reverses)
M*(delta V)/t = 1369*[10-(-1.9)]/0.18
= 9.05*10^4 kg m/s