A compact car, mass 730 kg, is moving at 1.00 ✕ 102 km/h toward the east. The driver of the compact car suddenly applies the brakes hard for 1.9 s. As a result, an average force of 4.8 ✕ 103 N is exerted on the car to slow it down. What is the momentum now?
To solve this problem, we can use the formula for momentum:
Momentum (p) = mass (m) × velocity (v)
Given:
Mass of the car (m) = 730 kg
Initial velocity of the car (v) = 1.00 × 10^2 km/h = (1.00 × 10^2 × 1000) m/s = 1.00 × 10^5 m/s
Time taken to apply brakes (t) = 1.9 s
Force exerted on the car (F) = 4.8 × 10^3 N
First, let's calculate the change in velocity using Newton's second law of motion:
F = (mass × change in velocity) / time
Rearranging the formula to find the change in velocity:
change in velocity = (F × time) / mass
change in velocity = (4.8 × 10^3 N × 1.9 s) / 730 kg
change in velocity = 12.48 m/s
Next, calculate the final velocity of the car by subtracting the change in velocity from the initial velocity:
final velocity = initial velocity - change in velocity
final velocity = 1.00 × 10^5 m/s - 12.48 m/s
final velocity = 9.8752 × 10^4 m/s
Now, we can calculate the momentum using the formula:
Momentum (p) = mass (m) × velocity (v)
momentum = 730 kg × 9.8752 × 10^4 m/s
momentum = 7.2052 × 10^7 kg m/s
Therefore, the momentum of the car after applying the brakes is 7.2052 × 10^7 kg m/s.
To find the momentum of the car after the brakes are applied, we need to first calculate the initial momentum before the brakes are applied and then calculate the final momentum after the brakes.
1. Calculate the initial momentum:
Momentum (p) is given by the formula: p = mass × velocity
Given:
Mass of the car (m) = 730 kg
Velocity of the car (v) = 1.00 ✕ 10^2 km/h
To calculate the initial momentum, we need to convert the velocity from km/h to m/s since the SI unit of momentum is kg·m/s.
Velocity in m/s = (Velocity in km/h) × (1000 m/1 km) × (1 h/3600 s)
Substituting the given values:
Velocity in m/s = (1.00 ✕ 10^2 km/h) × (1000 m/1 km) × (1 h/3600 s)
Velocity in m/s = (100000 m/3600 s)
Velocity in m/s ≈ 27.78 m/s
Now, calculate the initial momentum:
Initial momentum = mass × velocity
Initial momentum = 730 kg × 27.78 m/s
2. Calculate the final momentum:
The braking force applied on the car causes it to slow down, so the velocity decreases to 0 m/s.
Final momentum = mass × velocity
Final momentum = 730 kg × 0 m/s
Final momentum = 0 kg·m/s
Therefore, the momentum of the car after the brakes are applied is 0 kg·m/s.
Vo = 100km/h = 100,000m/3600s. = 27.8 m/s.
a = F/m = -4800/730 = -6.58 m/s^2.
V = Vo + a*t = 27.8 - 6.58*1.9 = 15.3 m/s.
Momentum = m*V = 730 * 15.3 = 11,174