Question

newton: force and motion, continued

1. how much force is needed to move a 0.1 kg snowball at a rate of 15 m/s² upward?
2. a 0.02 n push accelerates a table - tennis ball along a table at 8 m/s² north. what is the mass of the ball?
3. at lift - off, an astronaut on the space shuttle experiences an acceleration of approxi - mately 35 m/s² upward. what force does an 80 kg astronaut experience during this acceleration?
4. what is the acceleration of a train with a mass of 3.2×10⁹ kg that pushes itself for - ward with 2.4×10¹⁰ n of force?

Explanation:

Step1: Use Newton's second law \(F = ma\)

For problem 3: \(m = 0.1\space kg\), \(a=15\space m/s^{2}\). Then \(F = ma=0.1\times15\)

Step2: Calculate the value

\(F = 1.5\space N\)

For problem 4: \(F = 0.02\space N\), \(a = 8\space m/s^{2}\). From \(F=ma\), we get \(m=\frac{F}{a}=\frac{0.02}{8}\)

Step3: Calculate the value

\(m = 0.0025\space kg\)

For problem 5: \(m = 80\space kg\), \(a = 35\space m/s^{2}\). Using \(F=ma\), \(F=80\times35\)

Step4: Calculate the value

\(F = 2800\space N\)

For problem 6: \(F = 2.4\times 10^{10}\space N\), \(m = 3.2\times 10^{9}\space kg\). From \(F = ma\), \(a=\frac{F}{m}=\frac{2.4\times 10^{10}}{3.2\times 10^{9}}\)

Step5: Calculate the value

\(a = 7.5\space m/s^{2}\)

Answer:

1. \(1.5\space N\)
2. \(0.0025\space kg\)
3. \(2800\space N\)
4. \(7.5\space m/s^{2}\)