A car of mass 1100 kg, moving with a speed of 73 mph on a highway, passes a small SUV with a mass
1
1
2
times bigger, moving at 1/2 of the speed of the car.
(a) What is the ratio of the momentum of the SUV to that of the car?
pSUV
pcar
= 1
(b) What is the ratio of the kinetic energy of the SUV to that of the car?
KSUV
Kcar
=
Why are you changing names wth each question?
To solve this problem, we first need to calculate the momentum and kinetic energy of both the car and the SUV.
(a) Momentum is defined as the product of mass and velocity. The momentum of an object can be calculated using the formula:
momentum = mass × velocity
Given:
Mass of the car = 1100 kg
Speed of the car = 73 mph
Mass of the SUV = 1.5 × mass of the car = 1.5 × 1100 kg = 1650 kg
Speed of the SUV = 1/2 speed of the car = (1/2) × 73 mph = 36.5 mph
To compare the ratios, we can divide the momentum of the SUV by the momentum of the car:
Ratio of momentum = pSUV / pcar
First, let's convert the speeds from mph to m/s, as the SI unit for mass is kilograms and velocity is meters per second:
Speed of the car = 73 mph × (0.447 m/s) / (1 mph) = 32.615 m/s
Speed of the SUV = 36.5 mph × (0.447 m/s) / (1 mph) = 16.3275 m/s
Next, calculate the momentum for each object:
Momentum of the car = mass of the car × speed of the car = 1100 kg × 32.615 m/s
Momentum of the SUV = mass of the SUV × speed of the SUV = 1650 kg × 16.3275 m/s
Now, divide the momentum of the SUV by the momentum of the car to find the ratio:
Ratio of momentum = (Momentum of the SUV) / (Momentum of the car)
(b) Kinetic energy is defined as one-half of the product of mass and the square of velocity. The kinetic energy of an object can be calculated using the formula:
kinetic energy = (1/2) × mass × velocity^2
To compare the ratios, we can divide the kinetic energy of the SUV by the kinetic energy of the car:
Ratio of kinetic energy = KSUV / Kcar
Calculate the kinetic energy for each object:
Kinetic energy of the car = (1/2) × mass of the car × (speed of the car)^2
Kinetic energy of the SUV = (1/2) × mass of the SUV × (speed of the SUV)^2
Finally, divide the kinetic energy of the SUV by the kinetic energy of the car to find the desired ratio:
Ratio of kinetic energy = (Kinetic energy of the SUV) / (Kinetic energy of the car).
Now, you can substitute the values into the formulas and solve for the desired ratios.