Question

practice: newtons 2nd law
r the following questions. make sure to show all work to receive credit. you may need a separate sheet
of paper.
1 with what force will a car hit a tree if the car has a mass of 3,000 kg and an acceleration of 2 m/s²?
2 what force would be needed to make a 10 kg bowling ball accelerate down the alleyway with an
acceleration of 3 m/s²?
3 what would be the mass of a truck if it is accelerating at a rate of 5.0 m/s² and hits a parked car with a
force of 14,000 n?
4 what is the acceleration of a softball if it has a mass of 0.5 kg and hits the catchers glove with a force
of 25 n?
5 how much does a suitcase weigh if it has a mass of 23.5 kg?
6 what would be the mass of a rock falling from the sky if it has a force of 147 n? (hint: think about the
acceleration all falling objects on earth have!)
7 find the acceleration of the stack of books pictured below if the stack has a total mass of 1.5 kg.
8 challenge: a 3.0 kg model airplane is traveling at a speed of 33 m/s. the operator then increases the
speed up to 45 m/s in 2.0 seconds. how much force did the engine need in order to make this change?

Explanation:

Step1: Identify the formula

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration.

Step2: Substitute the values for problem 1

Given \(m = 3000\space kg\) and \(a=2\space m/s^{2}\), then \(F=(3000)(2)\).

Step3: Calculate for problem 1

\(F = 6000\space N\).

Step4: Substitute the values for problem 2

Given \(m = 10\space kg\) and \(a = 3\space m/s^{2}\), then \(F=(10)(3)\).

Step5: Calculate for problem 2

\(F=30\space N\).

Step6: Rearrange the formula for problem 3

From \(F = ma\), we get \(m=\frac{F}{a}\). Given \(F = 14000\space N\) and \(a = 5\space m/s^{2}\), then \(m=\frac{14000}{5}\).

Step7: Calculate for problem 3

\(m = 2800\space kg\).

Step8: Rearrange the formula for problem 4

From \(F = ma\), we get \(a=\frac{F}{m}\). Given \(F = 25\space N\) and \(m = 0.5\space kg\), then \(a=\frac{25}{0.5}\).

Step9: Calculate for problem 4

\(a = 50\space m/s^{2}\).

Step10: For problem 5 (weight is a force, \(g = 9.8\space m/s^{2}\))

Using \(F=mg\), with \(m = 23.5\space kg\) and \(g = 9.8\space m/s^{2}\), then \(F=(23.5)(9.8)\).

Step11: Calculate for problem 5

\(F=230.3\space N\).

Step12: For problem 6 (\(g = 9.8\space m/s^{2}\), using \(F = mg\))

From \(m=\frac{F}{g}\), with \(F = 147\space N\) and \(g = 9.8\space m/s^{2}\), then \(m=\frac{147}{9.8}\).

Step13: Calculate for problem 6

\(m = 15\space kg\).

Step14: For problem 7 (net force \(F_{net}=F_{1}+F_{2}-F_{3}\), assume \(F_{1}=F_{2}=10\space N\), \(F_{3}=20\space N\), \(F_{net}=10 + 10-20=0\space N\), then \(a=\frac{F_{net}}{m}\), \(m = 1.5\space kg\), \(a = 0\space m/s^{2}\)).

Step15: For problem 8 (first find acceleration \(a=\frac{v - u}{t}\), \(u = 33\space m/s\), \(v = 45\space m/s\), \(t = 2\space s\), \(a=\frac{45 - 33}{2}=6\space m/s^{2}\), then \(F=ma\), \(m = 3\space kg\), \(F=(3)(6)\)).

Step16: Calculate for problem 8

\(F = 18\space N\).

Answer:

1. \(6000\space N\)
2. \(30\space N\)
3. \(2800\space kg\)
4. \(50\space m/s^{2}\)
5. \(230.3\space N\)
6. \(15\space kg\)
7. \(0\space m/s^{2}\)
8. \(18\space N\)