How Is Speed Accuracy Measured in Bicycle Computers?

[ihat2]

i have these questions for homework and they been bugging me any help on working them out will be greatly appreciated

1. Speed is displayed on a bicycle computer to within 0.1 km/hr (about 0.03 m/s). However we are puzzled how this accuracy is obtained.
Measurements are updated each second, and assumed to be taken over 1 second intervals; the circumference of the tyre is 4.31 m (assume that the 1 s time interval and the circumference are both precise values).
Based on the fact that the rotation of the wheel is detected by a magnet on one spoke passing a detector on the front fork, what is the uncertainty, in m/s, of the displayed speed?
Answer to 2 significant figures please.

2. A toy rocket using compressed air and water is fired at an angle of 60º to the horizontal, with launch speed of 34 m/s. It returns to Earth some distance away, coincidentally at the same angle and speed (its propulsion reactivated on the way down - pity about the damage on impact). The time from launch to landing was 5.7 second.
What is the magnitude of its mean acceleration during the flight, in m/s 2?

3. A light spring is compressed by pushing it at each end. The force applied at each end is 40 Newton (which can be verified by using a force gauge). What is the tension (in Newton) in the middle of the spring?

 

[ihat2]

sorry this question as well
A spring balance is attached to 2 strings with hanging masses of 1 kg as shown . Assuming g = 10 m/s2 and the pulleys are frictionless, what is the reading on the spring balance, in Newton?

the attached file shows the diagram

 

[Chen]

Originally posted by ihat2
sorry this question as well
A spring balance is attached to 2 strings with hanging masses of 1 kg as shown . Assuming g = 10 m/s2 and the pulleys are frictionless, what is the reading on the spring balance, in Newton?

the attached file shows the diagram

See attachment... each of the two masses are in equilibrium, since they are equal. Therefore $$T_1 = m_1g$$ and $$T_2 = m_2g$$. Can you finish the problem?

 

[Chen]

Originally posted by ihat2
2. A toy rocket using compressed air and water is fired at an angle of 60º to the horizontal, with launch speed of 34 m/s. It returns to Earth some distance away, coincidentally at the same angle and speed (its propulsion reactivated on the way down - pity about the damage on impact). The time from launch to landing was 5.7 second.
What is the magnitude of its mean acceleration during the flight, in m/s 2?

Ehh, why should the rocket be accelerated during the flight? Assuming energy is preserved, and no other forces operate on the rocket, its kinetic energy at launch and land is equal. The launch velocity and final velocity are exactly the same, without having to accelerate the rocket while it's in the air.

If you don't know about energies yet, you should know that the rocket's trajectory is a parabola, and that the derivative of the parabola is the velocity. The absolute values of the derivative of a parabola, in two points with the same Y value, is equal.

 

[HallsofIvy]

"Ehh, why should the rocket be accelerated during the flight? "

Because that is the nature of rockets!

A rocket, unlike a thrown rock, has an engine on board that gives it force, and so acceleration, as it is flying. Energy is not conserved because the rocket burns chemical fuel while flying.

 

[Doc Al]

Originally posted by Chen
Ehh, why should the rocket be accelerated during the flight? Assuming energy is preserved, and no other forces operate on the rocket, its kinetic energy at launch and land is equal. The launch velocity and final velocity are exactly the same, without having to accelerate the rocket while it's in the air.

As HallsofIvy said, the rocket has a propulsion system. But even if it had none, it would still be accelerated. Gravity, you know.

I think this was meant as an exercise in computing average acceleration:
$$\vec{a}_{ave} = \frac {\Delta \vec{v}}{\Delta t}$$

 

[Chen]

Originally posted by HallsofIvy
"Ehh, why should the rocket be accelerated during the flight? "

Because that is the nature of rockets!

A rocket, unlike a thrown rock, has an engine on board that gives it force, and so acceleration, as it is flying. Energy is not conserved because the rocket burns chemical fuel while flying.

Obviously rockets are accelerated in the air, but in this specific case, in which it returns to land with the exact same velocity vector it took off with, acceleration is not needed (and if it was accelerated, a lot of energy has been wasted because the outcome is identical to that if it hadn't been accelerated).

 

[ihat2]

so for the rocket question is it using the 34 or he horizontal speed?
and for the spring tension is the answer 10?

 

[Chen]

Originally posted by ihat2
and for the spring tension is the answer 10?

20N I would think, as each mass is 10kg so the gravitational force on each of them is 10N.

 

[Doc Al]

Originally posted by Chen
20N I would think, as each mass is 10kg so the gravitational force on each of them is 10N.

No, the tension in the strings is 10N. This is what the spring scale would measure.