A 200 pound go-kart with a speed of 20 miles/hour collides with a 2nd go-kart (that was at rest) and causes it to move at a speed of 15 miles per hour. What is the mass of the 2nd cart if the first kart came to a stop upon collision?
To find the mass of the second go-kart, we can use the principle of conservation of momentum.
The formula for momentum is:
\( \text{Momentum} = \text{Mass} \times \text{Velocity} \)
According to the problem, the initial momentum of the first go-kart is \(200 \text{ lb} \times 20 \text{ mi/h}\), and the momentum of the second go-kart after the collision is \( \text{Mass}_2 \times 15 \text{ mi/h} \). Since the first go-kart comes to a stop upon collision, its final momentum is zero.
Using the principle of conservation of momentum, we can set up the equation:
\( \text{Initial momentum} = \text{Final momentum} \)
\( (200 \text{ lb} \times 20 \text{ mi/h}) = ( \text{Mass}_2 \times 15 \text{ mi/h}) + 0\)
Now let's convert the mass of the first go-kart from pounds to an equivalent mass in a unit such as grams or kilograms. Let's assume that 1 pound is equal to approximately 0.4536 kilograms.
So, the mass of the first go-kart is \(200 \text{ lb} \times 0.4536 \text{ kg/lb}\).
Now we can substitute the values into the equation:
\( (200 \times 0.4536 \text{ kg}) \times 20 \text{ mi/h} = \text{Mass}_2 \times 15 \text{ mi/h} \)
Simplifying the equation:
\( (90.72 \text{ kg} \times 20 \text{ mi/h}) = \text{Mass}_2 \times 15 \text{ mi/h} \)
\( 1814.4 \text{ kg mi/h} = \text{Mass}_2 \times 15 \text{ mi/h} \)
Now divide both sides of the equation by 15 mi/h:
\( \frac{{1814.4 \text{ kg mi/h}}}{{15 \text{ mi/h}}} = \text{Mass}_2 \)
After performing the division, we find that the mass of the second go-kart is approximately 120.96 kg.
So, the mass of the second go-kart is approximately 120.96 kg.