Question

A 15,680 n car, initially traveling at 20 m/s, applies a braking force of 640 n. the car comes to a complete stop. calculate the car’s change in momentum in [kg m/s]

Answer 1

The change in momentum of the car is -32,000 kg·m/s; this negative value indicates a decrease in the car's momentum in its initial direction of motion.

Step-by-step explanation:

To calculate the car’s change in momentum, we use the formula Δp = m • Δv, where Δp is the change in momentum, m is the mass of the object, and Δv is the change in velocity. Given that the car has a mass of 15,680 N (we will presume that this is a mistake and that it is actually the weight of the car, hence the mass m = 1,600 kg, given that weight=mass × gravity and approximating gravity as 9.8 m/s²), and it comes to a complete stop from an initial velocity of 20 m/s, the final velocity is 0 m/s. Therefore, the change in velocity Δv is -20 m/s (since it's coming to a stop). Using the mass m = 15,680 N / 9.8 m/s², which gives us approximately 1,600 kg, the change in momentum Δp is 1,600 kg • (-20 m/s) = -32,000 kg·m/s. The negative sign indicates that the momentum has decreased in the direction the car was initially moving.

Answer 2

The car's change in momentum is approximately
`\(313,728 \, \text{kg m/s}\).`

The change in momentum
`(\(\Delta p\))` of the car can be calculated using the equation:

`\[\Delta p = \text{Force} * \text{Time}\]`

First, calculate the time taken for the car to stop using the formula:

`\[ \text{Force} = \text{mass} * \text{acceleration} \]`

`\[ \text{acceleration} = \frac{\text{Force}}{\text{mass}} \]`

Given:

`\(\text{Force} = 640 \, \text{N}\)`

`\(\text{mass} = 15,680 \, \text{N}\)`

`\[\text{Acceleration} = \frac{640 \, \text{N}}{15,680 \, \text{kg}} \approx 0.0408 \, \text{m/s}^2\]`

The car starts at 20 m/s and decelerates uniformly to come to a stop. The formula to find the time taken is:

`\[ \text{Time} = \frac{\text{Change in Velocity}}{\text{Acceleration}} \]`

`\[ \text{Change in Velocity} = 20 \, \text{m/s} - 0 \, \text{m/s} = 20 \, \text{m/s} \]`

`\[ \text{Time} = \frac{20 \, \text{m/s}}{0.0408 \, \text{m/s}^2} \approx 490.2 \, \text{s}\]`

Now, calculate the change in momentum:

`\[\Delta p = \text{Force} * \text{Time}\]`

`\[\Delta p = 640 \, \text{N} * 490.2 \, \text{s}\]`

`\[\Delta p \approx 313,728 \, \text{kg m/s}\]`