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....
Let me see your work.
To calculate the speed of the sports car at impact, we can use the principles of conservation of momentum and the work-energy theorem.
Here's how you can solve this problem step by step:
Step 1: Find the initial velocity of the SUV (which is stopped at the red light). Since it is stopped, the initial velocity is 0 m/s.
Step 2: Calculate the total mass of the system. The total mass of the system is the sum of the masses of the sports car (930 kg) and the SUV (2500 kg), which is 930 kg + 2500 kg = 3430 kg.
Step 3: Use the work-energy theorem to find the work done by the friction force between the tires of the cars and the road. The work done is equal to the change in kinetic energy. Since the initial kinetic energy is 0 (the SUV is stopped) and the final kinetic energy is also 0 (both cars come to a stop), the work done by friction is equal to the initial kinetic energy. Therefore, the work done by friction is 0.5 * 3430 kg * v^2, where v is the speed of the sports car at impact (which we are trying to find).
Step 4: Calculate the force of friction. The force of friction can be found using the equation F_friction = coefficient of kinetic friction * normal force. The normal force acting on the cars is equal to the weight of the cars, which is equal to their masses multiplied by the acceleration due to gravity (9.8 m/s^2). The normal force is (930 kg + 2500 kg) * 9.8 m/s^2 = 34330 N. Therefore, the force of friction is 0.80 * 34330 N = 27464 N.
Step 5: Calculate the work done by friction using the formula W = F * d, where W is the work done, F is the force of friction, and d is the distance the cars skid before stopping (2.6 m).
Step 6: Set the work done by friction (calculated in Step 3) equal to the work done by friction (calculated in Step 5) and solve for the speed v.
0.5 * 3430 kg * v^2 = 27464 N * 2.6 m
Step 7: Solve the equation from Step 6 for v.
v^2 = (27464 N * 2.6 m) / (0.5 * 3430 kg)
v^2 = 13352.8 Nm / 1715 kg
v^2 = 7.7865 m^2/s^2
Taking the square root of both sides:
v = √(7.7865 m^2/s^2)
v ≈ 2.79 m/s
Therefore, the speed of the sports car at impact is approximately 2.79 m/s.
Vi= sqrt(2*.8*3430*2.6)/930
Vi= 3.9