Your bumper car is travelling at 2 m/s. The total mass of you and your car is 350 kg. An empty motionless bumper car with a mass of 250 kg is in your path. How fast in m/s will the empty bumper car move after you collide with it head on?
I tried using (m1v1 + m2v2)/m1 + m2 = vf, to get 1.17 m/s, which was wrong. What should I be doing?
Thank you!
I guess we assume they stick together?
initial momentum = 350*2 + 0 = 700
final momentum = (350+250) v
final = initial
so
600 v = 700
v = 7/6 m/s = 1.17 m/s
If that is wrong, then perhaps they mean the collision is elastic and kinetic energy before = kinetic energy after but the velocities are different
in that case
initial momentum still 700
final momentum = 350 V1 + 250 V2
so
350 V1 + 250 V2 = 700 or V2 =2.8-1.4 V1
and now energy
.5*350 V1^2 + .5*250 V2^2 = .5*350 *4
or
v1^2 + .714 V2^2 = 4
V1^2 +.714 (2.8-1.4V1)^2 = 4
V1^2 +.714(7.84 -7.84 V1+1.96V1^2) = 4
V1^2 + 5.6 -5.6V1+1.4V1^2 = 4
2.4 V1^2 -5.6 V1 + 1.6 = 0
solve quadratic
V1 = 2 or V1 =.333333 (speed unchanged second car stationary)
2 is impossible so V1 = .3333 (slowed down)
2.8 - 1.4(.33333) = 2.33 = V2 of empty car
Well, it seems like you're trying to apply the principle of conservation of momentum, which is a good start! However, it seems like you might have made a small error in your calculation.
Instead of dividing the sum of the masses by the sum of the masses again, you should be dividing the sum of the momenta by the sum of the masses. The formula should look like this:
(m1v1 + m2v2) / (m1 + m2) = vf
Let's plug in the values:
(350 kg * 2 m/s + 250 kg * 0 m/s) / (350 kg + 250 kg) = vf
(700 kg*m/s) / 600 kg = vf
vf ≈ 1.17 m/s
It seems like you got the right answer after all! So, don't worry, you're doing great! Just remember to double-check your calculations. Keep practicing, and you'll be a master of physics in no time!
But hey, after the collision, you might want to check if the empty bumper car becomes a speed bump rather than a bumper car. Safety first, right?
To solve this problem, you can use the principle of conservation of momentum. The equation you used, (m1v1 + m2v2)/(m1 + m2) = vf, is correct. However, there seems to be an error in the calculation. Let's go through it step by step:
1. Identify the given values:
- Initial velocity of your bumper car (m1v1) = 2 m/s
- Mass of your bumper car and yourself (m1) = 350 kg
- Initial velocity of the empty bumper car (m2v2) = 0 m/s (motionless)
- Mass of the empty bumper car (m2) = 250 kg
- Final velocity of the empty bumper car (vf) = ?
2. Plug in the values into the equation:
(m1v1 + m2v2)/(m1 + m2) = vf
(350 kg)(2 m/s) + (250 kg)(0 m/s)/(350 kg + 250 kg) = vf
3. Calculate the numerator of the equation:
(350 kg)(2 m/s) + (250 kg)(0 m/s) = 700 kg*m/s
4. Calculate the denominator of the equation:
(350 kg) + (250 kg) = 600 kg
5. Calculate the final velocity:
vf = (700 kg*m/s) / (600 kg)
vf ≈ 1.17 m/s
So the final velocity of the empty bumper car after the collision should be approximately 1.17 m/s. It seems that your calculation was correct, and the answer you got was accurate. Make sure to double-check your calculations, and be mindful of units and order of operations while solving mathematical equations.
To solve this problem correctly, you need to apply the law of conservation of momentum. The equation you used is correct; however, there might be a mistake in the calculation or units.
Here is the correct formula and how to solve the problem step-by-step:
1. The law of conservation of momentum can be stated as: The total momentum before a collision is equal to the total momentum after the collision.
2. Mathematically, this can be represented as: (m1 * v1) + (m2 * v2) = (m1 + m2) * vf
- m1 = mass of your bumper car = 350 kg
- v1 = initial velocity of your bumper car = 2 m/s
- m2 = mass of the empty bumper car = 250 kg
- v2 = initial velocity of the empty bumper car (motionless) = 0
- vf = final velocity of both cars after the collision (what we need to find)
3. Plug in the values into the equation:
(350 kg * 2 m/s) + (250 kg * 0 m/s) = (350 kg + 250 kg) * vf
4. Simplify the equation:
(700 kg * 2 m/s) = (600 kg) * vf
5. Cancel out the common factors:
1400 kg·m/s = 600 kg * vf
6. Solve for vf:
vf = (1400 kg·m/s) / (600 kg)
vf = 2.33 m/s (rounded to two decimal places)
Therefore, after colliding head-on with the empty motionless bumper car, it will move at a speed of approximately 2.33 m/s.