Please Help!!!
A 920 kg sports car collides into the rear end of a 2300 kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.5 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.42, calculates the speed of the sports car at impact. What was that speed?
first, find from momentum the speed of the two cars just after impact.
920V=(920+2300)Vi
or Vi= 920/(3220) V
Now,
vf^2=0=Vi^2+2ad
where a= F/m= mu*(3220)g/3220
Vi^2=.42g*2.5
Find Vi, then put it in
V= Vi(3220/920)
I got that vi=10.29 then when I sub in I get that v=11.23 but this is the wrong answer. Am I doing something wrong?
You forgot to put the 2 back in when finding Vi.
It says Vi^2= 0.42*g*2.5
It should be Vi^2= 2*0.42*g*2.5
That should take care of the wrong answers you come up with. (I know this is kind of late to answer your question but it might help someone else later on.)
@Ryan, is the "g" just gravity? Why do we need gravity in this equation? I keep doing this problem and getting the initial speed to 3.6 m/s which is not right.
To calculate the speed of the sports car at impact, we can make use of the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
This can be expressed as:
(mass of sports car * speed of sports car before collision) + (mass of SUV * speed of SUV before collision) = (mass of sports car * speed of sports car after collision) + (mass of SUV * speed of SUV after collision)
In this case, the SUV is at rest before the collision, so its initial velocity is zero. Therefore, the equation can be simplified:
mass of sports car * speed of sports car before collision = mass of sports car * speed of sports car after collision
Now we can plug in the given values:
mass of sports car = 920 kg
mass of SUV = 2300 kg
We need to find the speed of the sports car after the collision. However, we are given that the cars skid forward before stopping, indicating that the friction between the tires and the road played a role in bringing the cars to a halt. This friction force should be taken into account.
The friction force can be calculated using the equation:
friction force = coefficient of kinetic friction * normal force
The normal force can be calculated as the weight of the object:
normal force = mass * acceleration due to gravity
Now we can calculate the frictional force:
friction force = (coefficient of kinetic friction) * (mass of sports car) * (acceleration due to gravity)
To bring the cars to a halt, the frictional force must be equal to the total force exerted on the cars, which is the product of the mass of the cars and the acceleration:
friction force = (mass of sports car + mass of SUV) * (acceleration)
The acceleration can be found using the equation:
acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)
In this case, the initial velocity is the speed of the sports car before the collision, and the final velocity is zero, as the cars skid to a stop.
Now we can rearrange the equation to solve for the speed of the sports car before the collision:
speed of sports car before collision = sqrt((2 * distance * acceleration) + (0^2))
Plugging in the given values:
distance = 2.5 m
acceleration = friction force / (mass of sports car + mass of SUV)
Substituting the values into the equation and solving for the speed of the sports car before the collision will give you the answer.