A 930 kg sports car collides into the rear end of a 2500 kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.6 m before stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact.
what was the speed?
I just had someone answer this for me, but I did not get the correct answer....
Physics - bobpursley, Sunday, October 24, 2010 at 5:51pm
Let me see your work.
Vi= sqrt(2*.8*3430*2.6)/930
Vi= 3.9
To calculate the speed of the sports car at impact, you can use the principle of conservation of momentum. Before the collision, the SUV is stationary, so its initial momentum is zero. The momentum of an object is given by the product of its mass and velocity.
Let v1 be the velocity of the sports car before the collision and v2 be the velocity of the SUV after the collision. The conservation of momentum equation is:
(m1 * v1) + (m2 * v2) = 0
Where m1 is the mass of the sports car (930 kg) and m2 is the mass of the SUV (2500 kg).
Since the SUV is locked and stopped, its velocity (v2) is zero. Rearranging the equation, we can solve for v1:
v1 = -(m2 * v2) / m1
v1 = 0 / 930
Therefore, the initial velocity of the sports car (v1) is also zero.
However, this is not the final answer. The provided answer of 3.9 is incorrect. To find the correct answer, we need to consider the additional information about the cars skidding forward.
When the brakes are locked, the cars skid due to the force of kinetic friction. The work done by friction can be calculated using the equation:
Work = force * distance
The force of kinetic friction is given by the product of the coefficient of kinetic friction (0.80) and the normal force, which is the weight of the car (mass * gravity). In this case, the weight can be calculated using the formula:
Weight = mass * gravity
The distance traveled by the cars during skidding is given as 2.6 m.
The work done by friction can be equated to the change in kinetic energy of the cars:
Work = ΔKE
Since the final velocity of both cars is zero, the change in kinetic energy is equal to the initial kinetic energy. The initial kinetic energy can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Setting up the equations and substituting the given values:
Work = ΔKE
(force * distance) = (1/2) * (mass of sports car) * (velocity of sports car)^2
(0.8 * (mass of sports car) * (gravity) * distance) = (1/2) * (mass of sports car) * (velocity of sports car)^2
Simplifying further:
0.8 * 9.8 * 930 * 2.6 = 0.5 * 930 * (velocity of sports car)^2
Solving for the velocity of the sports car:
(velocity of sports car)^2 = (0.8 * 9.8 * 930 * 2.6) / (0.5 * 930)
velocity of sports car = sqrt((0.8 * 9.8 * 930 * 2.6) / (0.5 * 930))
Calculating the above expression gives the correct answer for the speed of the sports car at impact.
To solve this problem, we can use the concept of conservation of momentum in a collision. The total momentum before the collision is equal to the total momentum after the collision.
Let's consider the sports car and SUV as an isolated system. The momentum of the sports car before the collision is given by:
m1 * v1
where m1 is the mass of the sports car (930 kg) and v1 is the initial velocity of the sports car.
Similarly, the momentum of the SUV before the collision is given by:
m2 * v2
where m2 is the mass of the SUV (2500 kg) and v2 is the initial velocity of the SUV (which is assumed to be zero in this case).
After the collision, the two cars are locked together and skid forward 2.6 m before stopping. The final velocity of the cars after the collision is zero. Therefore, the momentum after the collision is also zero.
Using the conservation of momentum, we can write the equation:
m1 * v1 + m2 * v2 = 0
Plugging in the given values, we have:
930 kg * v1 + 2500 kg * 0 = 0
930 kg * v1 = 0
v1 = 0
According to the calculations, the initial velocity of the sports car is zero, which means the car was not moving at the time of the collision. Please double-check the given information or calculations to ensure accuracy.