8.5: Chapter 8 Homework Problems
A 50-kg box is being pulled across a surface by a force of 200 N in the direction shown below. If the coefficient of friction is 0.3, what is the rate of acceleration of the box and how far will the box move in a three-second period?
- Solution
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\(a = 1.23 \, m/s^2\)
\(s = 5.52 \, m\)
A 3-kg cannonball is shot out of a cannon with an initial velocity of 300 m/s at a 25-degree angle. A headwind exerts a constant 5 N horizontal force. How far will the cannonball travel horizontally before hitting the ground?
- Solution
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\(d = 6470 \, m\)
A 1-kg block sits on a rotating table as shown below. If the static coefficient of friction is assumed to be 0.4, what is the maximum angular velocity \((\dot{\theta})\) that can be achieved before the block begins to slip?
- Solution
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\(\dot{\theta} = 1.4 \, \frac{rad}{s}\)
A 5-kg instrument is held via a cable to a space station. The instrument and space station are both rotating at a rate of 0.5 rad/s when the space station begins retracting the cable at a constant rate of 0.25 m/s.
- What is the tension in the cable at this instant?
- What will the angular acceleration \((\ddot{\theta})\) of the cable be? Hint: there are no forces in the \(\theta\) direction.
- Solution
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\(T = 15 \, N\)
\(\ddot{\theta} = 0.0208 \, \frac{rad}{s^2}\)