A 3000 kg truck moving with a velocity of 10 m/s hits a 1000 kg parked car. The impact causes the 1000 kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, what is the velocity of the truck immediately after the collision?
Question
A 3000 kg truck moving with a velocity of 10 m/s hits a 1000 kg parked car. The impact causes the 1000 kg car to be set in motion at 15 m/s. Assuming that momentum is conserved during the collision, what is the velocity of the truck immediately after the collision?
Solution
Sure, let's solve this step by step.
Step 1: Understand the principle of conservation of momentum. The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the truck and the car form an isolated system because they are the only two objects involved and we are assuming no external forces are acting on them (like friction, for example).
Step 2: Calculate the initial momentum of the system. The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). So, the initial momentum of the system is the momentum of the truck because the car is initially at rest.
Initial momentum = mass of truck * velocity of truck = 3000 kg * 10 m/s = 30000 kg*m/s
Step 3: Calculate the final momentum of the system. After the collision, both the truck and the car are moving. So, the final momentum of the system is the sum of the momentum of the truck and the car after the collision. We don't know the final velocity of the truck yet, but we can express it as:
Final momentum = mass of truck * velocity of truck (after collision) + mass of car * velocity of car (after collision) = 3000 kg * v (unknown) + 1000 kg * 15 m/s
Step 4: Set the initial momentum equal to the final momentum and solve for the unknown. According to the principle of conservation of momentum, the initial momentum should be equal to the final momentum. So:
30000 kgm/s = 3000 kg * v + 15000 kgm/s
Subtract 15000 kg*m/s from both sides to isolate v:
15000 kg*m/s = 3000 kg * v
Finally, divide both sides by 3000 kg to solve for v:
v = 15000 kg*m/s / 3000 kg = 5 m/s
So, the velocity of the truck immediately after the collision is 5 m/s.
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For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Momentum versus kinetic energy.Part AWhat is the magnitude of the momentum of a 12000 kgkg truck whose speed is 13.0 m/sm/s?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typep𝑝 =nothingnothingSubmitRequest AnswerPart BWhat speed would a 2200 kgkg SUV have to attain in order to have the same momentum?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =nothingnothingSubmitRequest AnswerPart CWhat speed would a 2200 kgkg SUV have to attain in order to have the same kinetic energy?Express your answer with the appropriate units.Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value typev𝑣 =
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