A Motorcycle And Rider Have A Total Mass Of 335 Kg
1 A Motorcycle And Rider Have A Total Mass Equal To 335 Kg The Rider
1. A motorcycle and rider have a total mass of 335 kg. The rider applies the brakes, causing the motorcycle to accelerate at a rate of −4 m/s2. What is the net force on the motorcycle? (Indicate the direction with the sign of your answer.)
Paper For Above instruction
The net force acting on an object can be calculated using Newton's second law of motion, expressed as Fnet = m × a, where m is the mass of the object and a is its acceleration. Given the total mass of the motorcycle and rider is 335 kg, and the acceleration is −4 m/s2, the calculation involves multiplying these values:
Fnet = 335 kg × (−4 m/s2) = −1340 N
The negative sign indicates that the force acts in the direction opposite to the motion (i.e., deceleration). Therefore, the net force exerted on the motorcycle is 1340 N directed opposite to the motorcycle's initial motion.
2. On aircraft carriers, catapults are used to accelerate jet aircraft...
2. On aircraft carriers, catapults are used to accelerate jet aircraft to flight speeds in a short distance. One such catapult takes a 17,800-kg jet from rest to 67 m/s in 2.7 seconds.
(a) What is the acceleration of the jet in m/s2?
The acceleration (a) can be found using the formula:
a = Δv / Δt = (vfinal - vinitial) / t = (67 m/s - 0) / 2.7 s ≈ 24.81 m/s2
(b) What is the acceleration of the jet in g's?
To convert acceleration into g's, divide by standard gravity (g ≈ 9.81 m/s2):
ag = 24.81 / 9.81 ≈ 2.53 g
(c) How far does the jet travel while it is accelerating?
The distance (d) covered during acceleration can be calculated as:
d = vinitial× t + 0.5× a × t2 = 0 + 0.5 × 24.81 × (2.7)2 ≈ 90.34 meters
3. An airplane is built to withstand a maximum acceleration of 7 g...
3. An airplane with a mass of 1,210 kg is designed to withstand a maximum acceleration of 7 g. To find the maximum force it can withstand:
F = m × a = 1210 kg × 7 × 9.81 m/s2 ≈ 83,051 N
4. Under certain conditions, the human body...
4. Under specific conditions, the human body can tolerate an acceleration of 10 g.
(a) What net force would have to act on someone with mass 75 kg to cause this acceleration?
F = m × a = 75 kg × 10 × 9.81 ≈ 7358 N
(b) First, find the weight of such a person in pounds. Second, convert the answer obtained in part (a) into pounds.
The weight in pounds: W = m × gEarth in pounds. Since 1 kg ≈ 2.20462 pounds, weight W = 75 kg × 2.20462 ≈ 165.3 pounds.
The force from part (a) in pounds: 7358 N. Knowing 1 N ≈ 0.22481 pounds-force, the force in pounds-force is: 7358 × 0.22481 ≈ 1654 pounds-force.
5. A race car rounds a curve at 55 m/s...
5. A race car with a mass of 685 kg is moving at 55 m/s around a curve with a radius of 434 m. Assuming constant speed, we analyze the centripetal acceleration and force.
(a) What is the car's (centripetal) acceleration?
ac = v2 / r = (55)2 / 434 ≈ 6.98 m/s2
(b) What is it in g's?
ag = 6.98 / 9.81 ≈ 0.713 g
(c) What is the centripetal force acting on the car?
Fc = m × ac = 685 kg × 6.98 ≈ 4788 N
6. As a baseball is being caught...
6. A baseball with a mass of 0.145 kg is caught after its speed drops from 27 m/s to zero in 0.008 seconds.
(a) What is the baseball's acceleration in m/s2?
a = Δv / Δt = (0 - 27) / 0.008 = -3375 m/s2
In terms of g's: ag = -3375 / 9.81 ≈ -344 g
What is the size of the force acting on it?
F = m × a = 0.145 kg × (−3375) ≈ −489.38 N
7. As a rocket ascends, its acceleration increases even though the net force on it stays constant...
7. The reason for increasing acceleration despite a constant net force is:
The second statement is correct: "The rocket's mass decreases as its fuel is consumed. The same net force acting on a smaller mass results in a larger acceleration." As fuel burns, the rocket's mass decreases, so the acceleration (a = F/m) increases even when the force remains unchanged.
References
- Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics. Cengage Learning.
- Hewitt, P. G. (2015). Conceptual Physics. Pearson.
- Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
- Walker, J. (2004). Physics (5th Edition). Pearson Education.
- Young, H. D., & Freedman, R. A. (2012). University Physics with Modern Physics. Pearson.
- Giancoli, D. C. (2014). Physics for Scientists and Engineers. Pearson.
- Chabay, R., & Sherwood, B. (2011). Matter & Interactions. Wiley.
- Feynman, R. P., Leighton, R. B., & Sands, M. (2010). The Feynman Lectures on Physics. Basic Books.
- Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.
- Kittel, C. (2004). Introduction to Solid State Physics. Wiley.