Question

part 4: use the equation for newtons second law of motion
for each of the following problems, solve for the missing variable (force, mass, or acceleration) using the equations from the previous page. be sure to include the appropriate units in your final answer.
① the mass of an object is 2 kg and its acceleration is 10 m/s². calculate the net force on the object.
② a roller - coaster car, with a mass of 500 kg, accelerates at a rate of 5 m/s². calculate the net force acting on the car.
③ a force of 30 n is applied to an object and causes it to accelerate at 6 m/s². calculate the mass of the object.
④ a bowling ball with a mass of 6.5 kg and is rolling down an alleyway with an acceleration of 2 m/s². calculate the force that was applied to the bowling ball.
⑤ an object is falling down in the sky at an acceleration of 9.8 m/s². the mass of the object is 180 kg. calculate the force the object will apply when it hits the ground.
⑥ a bull has a mass of 650 kg and charges a wall with a force of 975 n. calculate the acceleration of the bull when it hits the wall.
⑦ a 200 n force is applied to an object with a mass of 40 kg. calculate the acceleration of the object when the force is applied.
⑧ during a collision test, a truck hits a wall with 80,000 n of force. the initial velocity of the truck was m/s, the velocity of the truck when it hit the wall was 30 m/s, and it took 6 seconds from the time the truck started moving until it hit the wall. what was the mass of the truck? (hint: use the equation below to calculate the acceleration)
acceleration = (final velocity - initial velocity) / time

Explanation:

Step1: Recall Newton's second - law formula

Newton's second - law is $F = ma$, where $F$ is force in Newtons (N), $m$ is mass in kilograms (kg), and $a$ is acceleration in meters per second squared ($m/s^{2}$).

Problem 1

Given $m = 2$ kg and $a=10$ $m/s^{2}$.

Step2: Substitute values into formula

$F=ma=(2\ kg)\times(10\ m/s^{2}) = 20$ N

Problem 2

Given $m = 500$ kg and $a = 5$ $m/s^{2}$.

Step2: Substitute values into formula

$F=ma=(500\ kg)\times(5\ m/s^{2})=2500$ N

Problem 3

Given $F = 30$ N and $a = 6$ $m/s^{2}$.

Step2: Rearrange formula to solve for $m$

$m=\frac{F}{a}=\frac{30\ N}{6\ m/s^{2}} = 5$ kg

Problem 4

Given $m = 6.5$ kg and $a = 2$ $m/s^{2}$.

Step2: Substitute values into formula

$F=ma=(6.5\ kg)\times(2\ m/s^{2})=13$ N

Problem 5

Given $m = 180$ kg and $a = 9.8$ $m/s^{2}$ (approximate acceleration due to gravity).

Step2: Substitute values into formula

$F=ma=(180\ kg)\times(9.8\ m/s^{2}) = 1764$ N

Problem 6

Given $m = 650$ kg and $F = 975$ N.

Step2: Rearrange formula to solve for $a$

$a=\frac{F}{m}=\frac{975\ N}{650\ kg}=1.5$ $m/s^{2}$

Problem 7

Given $F = 200$ N and $m = 40$ kg.

Step2: Rearrange formula to solve for $a$

$a=\frac{F}{m}=\frac{200\ N}{40\ kg}=5$ $m/s^{2}$

Problem 8

First, find acceleration using $a=\frac{v - u}{t}$, where $v = 30$ m/s, $u$ (initial velocity is not given, assume $u = 0$ m/s for simplicity as the hint focuses on the time - to - impact phase), and $t = 6$ s.

Step1: Calculate acceleration

$a=\frac{30\ m/s-0\ m/s}{6\ s}=5$ $m/s^{2}$
Given $F = 80000$ N.

Step2: Rearrange $F = ma$ to solve for $m$

$m=\frac{F}{a}=\frac{80000\ N}{5\ m/s^{2}}=16000$ kg

Answer:

1. 20 N
2. 2500 N
3. 5 kg
4. 13 N
5. 1764 N
6. 1.5 $m/s^{2}$
7. 5 $m/s^{2}$
8. 16000 kg