Force & Mass
Practice
practice problem 1
A supertanker doesn't come with brakes. Using engines alone, it takes a loaded supertanker 13 km (8 miles) to stop. A typical vessel of this class has a gross mass of about 150 million kilograms (150 thousand tons) and a cruising speed of 50 kph (30 mph). Determine the average stopping force applied to the ship.
solution
This problem lends itself well to standard techniques. State the given quantities and convert them to SI units as needed. Solve the appropriate equation of motion to get the acceleration. Substitute this expression into Newton's second law and solve. It can also be solved using the work-energy theorem — as it will be in a later section of this book. Both methods lead to exactly the same answer — as they should.
Δs = | 13,000 m | |
m = | 150 × 10^{6} kg | |
v = | 0 m/s | |
v_{0} = | 50,000 m | = 13.888…m/s |
3,600 s | ||
F = | ? |
v^{2} = | v_{0}^{2} + 2aΔs | |||
a = | −v_{0}^{2} | = | −(13.888…m/s)^{2} | |
2Δs | 2(13,000 m) | |||
a = | −0.00742 m/s^{2} | |||
F = ma |
F = (150 × 10^{6} kg)(−0.00742 m/s^{2}) |
F = −1,110,000 N |
The first sentence of this question came from an article in the Chicago Tribune dated 6 April 2001, Strait with No Equal Has New Danger. Moral of the story: Yield to the supertanker when you're sailing the Bosphorus.
practice problem 2
A person stands in an elevator weighing a cheeseburger with a kitchen scale. (It could happen.) The mass of the cheeseburger is 0.150 kg. The scale reads 1.14 N.
- Draw a free body diagram showing all the forces acting on the cheeseburger.
- Determine the weight of the cheeseburger.
- Determine the magnitude and direction of the net force on the cheeseburger.
- Determine the magnitude and direction of the elevator's acceleration.
- At the time the person in the elevator is weighing the cheeseburger, the elevator's instantaneous velocity is upward. Is the speed of the elevator increasing, decreasing, or remaining constant at this moment? Justify your answer.
solution
Solutions…
- All objects have weight. Objects resting on solid surfaces also experience a normal force. Weight points down, since it always does. Normal points up, since the problem didn't say anything about the scale not being level. Draw a box with one arrow pointing up and another pointing down. Try to make the upward pointing arrow look smaller than the downward one. Label the upward pointing arrow "normal" and the downward pointing arrow "weight".
- Use the simple equation for weight. Assume the elevator is near the surface of the earth where gravity is around its standard value.
W = mg W = (0.150 kg)(9.8 m/s^{2}) W = 1.47 N - There are only two forces on the cheeseburger and they are opposite each other. This means the net force is the difference of the two forces. I think I will let up be the positive direction for this problem. The normal force is what the scale reads. Weight was computed in the previous part of this problem. The difference is negative, which means the net force is downward.
ΣF = N − W ΣF = 1.14 N − 1.47 N ΣF = −0.33 N down - Use Newton's second law of motion to determine the acceleration. The mass of the cheeseburger was given in the problem and we just computed the net force a moment ago. Net force and acceleration are always in the same direction, since the math says so. Acceleration is also downward.
a = ΣF m a = −0.33 N 0.150 kg a = −2.2 m/s^{2} down - The speed of the elevator is decreasing since the acceleration is opposite the velocity.
practice problem 3
Write something different.
solution
Answer it.
practice problem 4
Write something completely different.
solution
Answer it.