Question

the cool school rap
momentum
the measurement of mass in motion.
an objects momentum depends on its mass and velocity.
this relationship can be expressed in a formula-
momentum = mass × velocity
or
p = mv
refer to the illustrations to help you solve the following problems. use the space provided to show your work.
①examine the hill scene on the right. which cyclist would be harder to stop? why?
②if the elephant is moving at a velocity of 10 m/s, what is his momentum? ____(kg·m/s)
③if the squirrel is moving at a velocity of 15 m/s, what is his momentum? ____(kg·m/s)
④if the elephant is moving at a velocity of.5 m/s, and the squirrel is moving at a velocity of 600 m/s, which cyclist has more momentum? __ what is the momentum of each cyclist? elephant(kg·m/s) squirrel__(kg·m/s)
⑤the butterfly has a velocity of 4.5 m/s. what is his momentum? ____(kg·m/s)
⑥calculate the momentum of each cyclist if they were all traveling at a velocity of 13 m/s. elephant__(kg·m/s) squirrel(kg·m/s) human__(kg·m/s)
⑦how fast must each cyclist go in order to achieve a momentum of 360 kg·m/s? elephant__(m/s) squirrel(m/s) human__(m/s)

Explanation:

Step1: Recall momentum formula

The formula for momentum is $p = mv$, where $p$ is momentum, $m$ is mass and $v$ is velocity.

Step2: Answer question 1

The elephant - cyclist would be harder to stop because it has a much larger mass. According to $p = mv$, with a larger mass, for the same velocity, it has a larger momentum, and more force is needed to stop it.

Step3: Answer question 2

Given $m = 3000$ kg and $v=10$ m/s. Using $p = mv$, we have $p=3000\times10 = 30000$ kg·m/s.

Step4: Answer question 3

Given $m = 0.5$ kg and $v = 15$ m/s. Using $p=mv$, we get $p=0.5\times15=7.5$ kg·m/s.

Step5: Answer question 4

For the elephant, $m = 3000$ kg and $v = 0.5$ m/s, so $p_{elephant}=3000\times0.5 = 1500$ kg·m/s. For the squirrel, $m = 0.5$ kg and $v = 600$ m/s, so $p_{squirrel}=0.5\times600=300$ kg·m/s. The elephant - cyclist has more momentum.

Step6: Answer question 5

Given $m = 0.0002$ kg and $v = 4.5$ m/s. Using $p = mv$, we have $p=0.0002\times4.5 = 0.0009$ kg·m/s.

Step7: Answer question 6

For the elephant, $m = 3000$ kg and $v = 13$ m/s, $p_{elephant}=3000\times13=39000$ kg·m/s. For the squirrel, $m = 0.5$ kg and $v = 13$ m/s, $p_{squirrel}=0.5\times13 = 6.5$ kg·m/s. For the human, assume mass $m = 60$ kg and $v = 13$ m/s, $p_{human}=60\times13=780$ kg·m/s.

Step8: Answer question 7

Using $v=\frac{p}{m}$. For the elephant, $m = 3000$ kg and $p = 360$ kg·m/s, so $v=\frac{360}{3000}=0.12$ m/s. For the squirrel, $m = 0.5$ kg and $p = 360$ kg·m/s, so $v=\frac{360}{0.5}=720$ m/s. For the human, $m = 60$ kg and $p = 360$ kg·m/s, so $v=\frac{360}{60}=6$ m/s.

Answer:

1. The elephant - cyclist, because of its larger mass.
2. 30000 kg·m/s
3. 7.5 kg·m/s
4. The elephant - cyclist; 1500 kg·m/s (elephant), 300 kg·m/s (squirrel)
5. 0.0009 kg·m/s
6. 39000 kg·m/s (elephant), 6.5 kg·m/s (squirrel), 780 kg·m/s (human)
7. 0.12 m/s (elephant), 720 m/s (squirrel), 6 m/s (human)