Question

Suppose the two cars had rubber bumpers in the front and back – similar to the bumper cars children (of all ages!) ride at amusement parks. Also, suppose that the cars are sturdy enough that the metal they are made of does not bend during the collision. In this case, the cars would undergo a perfectly elastic collision. Assume just like in the first collision question that the SUV (initially moving to the right) collides into the stationary smart car.

After the collision, the smart car will obviously move to the
right. What about the SUV? (**Hint:** What do you
think would happen if the SUV was **much larger** than
the smart car, e.g., has a mass that is 50 times larger?)

The SUV will move to the right.

After the collision, which car do you think moves faster? Why?

The smart car because it has less mass.

Since this is a collision, momentum is conserved. Write down the momentum conservation equation for this situation. Mass of smart car = 1000 kg, mass of SUV = 4000 kg, initial speed of SUV = 15 m/s.

4v1 + v2 = 60

Is this equation sufficient to find the speeds of the two cars after the collision? Why or why not?

No because it includes two variables and we still need to find the speed after the collision.

What other quantity is conserved during a perfectly elastic collision? Write down the equation for that conservation.

1/2m1u1^{2}+1/2m2u2^{2} =
1/2m1v1^{2}+1/2m2v2^{2}

If you have not done so already, simplify the two equations (e.g., by dividing by 1000) and rewrite them here. If you have simplified them, just rewrite them here.

4v1+v2 = 60

4v1^{2}+v2^{2} =
900

A. Using these two equations it is possible to solve for both final speeds. However, the algebra is somewhat challenging because one of the equations has the final speeds of the two cars both squared. The book provides the general solutions to these equations in which you can plug in the initial speeds and the masses of the cars and obtain the final speeds. That won’t be necessary here. Instead, suppose someone measures the final speed of the SUV to be 9.0 m/s. What is the final speed of the smart car? You should get the same number if you use either equation, so make sure you use both.

Using the momentum equation Using the conservation of KE equation

B. Suppose that this collision also took 0.1 seconds. What is the magnitude of the net force acting on either car during the collision? How does this force compare to the perfectly inelastic collision? What is the acceleration acting on the smart car? On the SUV?

C. Generally how do elastic collisions compare to perfectly inelastic collisions? Discuss the forces being exerted on the cars, the accelerations and the kinetic energies.

Answer #1

The bumpers on cars are designes so that cars will bounce off
each other during low-speed collisions, causing less damage.
Consider a bumper test where a 1840 kg car traveling to the right
at 1.55 m/s collides with a 1310 kg car going to the left at 1.10
m/s . The test results show that the heavier car's speed just after
the collision was 0.280 m/s in its original direction. You can
ignore any road friction during the test crash....

Elastic collisions: one at rest one moving, two colliding, both
initially moving the same direction.
Inelastic collisions: one at rest one moving, two colliding,
both initially moving the same direction.
Perfectly elastic collisions: one at rest one moving, two
colliding, both initially moving the same direction.
Was momentum conserved for all types of collisions you examined
in this experiment? If not, explain the cause of losing or
gaining momentum. Was total velocity conserved for all types of
collisions you examined...

1.You are headed down a highway at 30.0m/s in your 1210 kg car
texting away on your phone when you just happen to look up and see
that you have crossed the centerline and are colliding with a 36300
kg truck going 30.0m/s in the opposite direction. Momentum is
conserved in all collisions. Sketch and label a diagram choosing
which direction is positive.
A.what is the total momentum of the two-vehicle system keeping
in mind that the momentum is a...

A car, mass m1 is moving to the right on a frictionless air
track. It collides with a second car, mass m2, which is initially
at rest. Which of the following statements are true? (If A and E
are true, and the others are not, enter TFFFT).
A) If car 1 is much lighter than m2, and the collision is
perfectly elastic, car 1 will continue heading to the right with
nearly its original speed after the collision.
B) If...

A car, mass m1 is moving to the right on a
frictionless air track. It collides with a second car, mass
m2, which is initially at rest. Which of the following
statements are true? (If A and E are true, and the others are not,
enter TFFFT).
A) If car 1 is much lighter than m2, and the collision is perfectly
elastic, car 1 will continue heading to the right with nearly its
original speed after the collision.
B) If...

When cars are equipped with flexible bumpers, they will bounce
off each other during low-speed collisions, thus causing less
damage. In one such accident, a 1800 kg car traveling to the right
at 1.40 m/s collides with a 1450 kg car going to the left at 1.10
m/s . Measurements show that the heavier car's speed just after the
collision was 0.260 m/s in its original direction. You can ignore
any road friction during the collision.
A-What was the speed...

A bumper car with mass m1 = 114 kg is moving to the
right with a velocity of v1 = 4.7 m/s. A second bumper
car with mass m2 = 94 kg is moving to the left with a
velocity of v2 = -3.7 m/s. The two cars have an elastic
collision. Assume the surface is frictionless.
1)What is the velocity of the center of mass of the system?
2)What is the initial velocity of car 1 in the center-of-mass...

Useful Formulae
potential
energy:
Uspr = ½ k (Dx)2
Conservation of Momentum:
p = mv;
m1v1 + m2v2 =
constant; p(initial) =
p(final);
For perfectly elastic collisions
ONLY:
(v1i – v2i) = - (v1f -
v2f)
k1 = (m1 – m2) / m1
+ m2; k2
= 2m2;
v1f = k1v1i +
k2v2i;
v2f = k2v1i +
k1v2i;
Rocket Equation
Thrust =
|dm/dt|*vexh;
vfinal = vinitial + vexh*ln
(Minitial / Mfinal);
[dm/dt] = kg/sec;
3. Perfectly Elastic Collision. Two masses...

A man of mass m1 = 64.5 kg is skating at v1 = 7.60 m/s behind
his wife of mass m2 = 53.0 kg, who is skating at v2 = 3.80 m/s.
Instead of passing her, he inadvertently collides with her. He
grabs her around the waist, and they maintain their balance.
(a) Sketch the problem with before-and-after diagrams,
representing the skaters as blocks.
(b) Is the collision best described as elastic, inelastic, or
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Two cars collide in an intersection: a 2200kg SUV that had been
headed East and a 1500kg sports car that had been headed North. The
cars deformed and remained together after colliding, sliding to
rest 5.0m from the crash. The angle from the crash to the resting
point is 35o N of E. Coefficient of sliding (kinetic)
friction is μ=0.80 for both vehicles. There are 8m long
skid marks leading into the intersection indicating that the
northbound car locked its...

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