In a crash test, a 2000-kg van collides with a concrete support. The stopping time interval for the collision is 0.10 s, and the impulse exerted by the support on the van is 7.0×103N⋅s.
A.) Determine the magnitude of the change in momentum.
B.)Determine the magnitude of the average force exerted by the concrete support on the van.
C.)If the van is constructed to collapse more during the collision so that the time interval during which the impulse is exerted is tripled, what is the magnitude of the average force exerted by the concrete support on the van?
a) ANSWER: 5.5 * 10^3 N*s
impulse = change in momentum; I = 5.5 *10^3 so the change in momentum = 5.5 * 10^3
B) ANSWER 55000 N
impulse = Faverage * time
5.5 * 10^3 = Faverage * (0.1)
5.5 * 10^4 = Faverage
C) ANSWER 18000 N
impulse = Faverage * time
Our new time is 0.3 (since 0.1 * 3 = 0.3)
5.5 * 10^3 = Faverage * (0.3)
1.8 * 10^4 = Faverage (Faverage decreases)
A.) Well, to determine the magnitude of the change in momentum, we just have to use the formula. But before we do that, let me tell you a joke. Why don't scientists trust atoms? Because they make up everything! Now, back to business. The formula for calculating the change in momentum is simply the impulse, which is equal to the change in momentum. So, the magnitude of the change in momentum is 7.0×10^3 N⋅s.
B.) Now, let's move on to the magnitude of the average force exerted by the concrete support on the van. Do you know what the support said to the van after the collision? "I've got you leaning on me!" Hilarious, isn't it? Anyway, we can find the average force by dividing the impulse by the stopping time interval. So, the magnitude of the average force exerted by the concrete support on the van is (7.0×10^3 N⋅s) / (0.10 s).
C.) Ah, the van wants to collapse more during the collision? It sure knows how to make an entrance! Now, if the time interval during which the impulse is exerted is tripled, we need to determine the new average force. Let's calculate it. The impulse is still the same, so we can use the formula from part B, but with the new time interval. So, the magnitude of the average force exerted by the concrete support on the van would be (7.0×10^3 N⋅s) / (0.10 s * 3).
I hope that helps, and remember, laughter is the best impulse!
A.) To determine the magnitude of the change in momentum, we can use the equation:
Change in Momentum = Impulse
Given that the impulse exerted by the support on the van is 7.0×10^3 N⋅s, the magnitude of the change in momentum is also 7.0×10^3 kg⋅m/s.
B.) To determine the magnitude of the average force exerted by the concrete support on the van, we can use the equation:
Impulse = Force × Time
Rearranging the equation, we get:
Force = Impulse / Time
Given that the impulse is 7.0×10^3 N⋅s and the time interval is 0.10 s, we can substitute the values to find:
Force = 7.0×10^3 N⋅s / 0.10 s
Force = 7.0×10^4 N
Therefore, the magnitude of the average force exerted by the concrete support on the van is 7.0×10^4 N.
C.) If the time interval during which the impulse is exerted is tripled, we need to find the new force exerted by the concrete support. Let's denote the new time interval as T.
Using the equation from part B:
Force = Impulse / T
Since we want to triple the time interval, the new time interval is 3 times the original time interval, which means T = 3 * 0.10 s = 0.30 s.
Substituting the values into the equation:
Force = 7.0×10^3 N⋅s / 0.30 s
Force ≈ 2.33×10^4 N
Therefore, if the time interval during which the impulse is exerted is tripled, the magnitude of the average force exerted by the concrete support on the van would be approximately 2.33×10^4 N.
a. impulse=changemomentum, you are given impulse, solve for change of momentum
b. force*time=impulse
avg force=impulse/time
c. avg force= impulse/(3*time)