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Chapter 4: Q47 P (page 168)

For this problem you will need measurements of the position vs. time of a block sliding on a table, starting with some initial velocity, showing down, and coming to rest. If you do not have an appropriate laboratory setup for making these measurements, your instructor will provide you with such data. Analyze these data to determine the coefficient of friction and to see how well they support the assertion that the force of sliding friction is essentially independent of the speed of sliding.

Short Answer

Expert verified

The coefficient of friction is determined by using a position vs. time graph which is essentially independent of the speed of sliding.

Step by step solution

01

Significance of coefficient of friction

  • The force needs to resist the movement of an objectis known asfrictional force
  • The parameter gotten from theposition vs time graph is velocity. If theslope is deeper, thenquicker the movement is changing.
  • The ratio of friction force to normal force is defined as the coefficient of friction
  • The coefficient of kinetic friction is defined asthe ratio of kinetic friction force to the normal force.
  • The coefficient of kinetic friction is defined asthe ratio of static friction force to the normal force.
  • The coefficient of static friction is known as the limiting friction which has the maximum value.
  • The coefficient of kinetic friction has the magnitude of the constant force which has less than the limiting friction.

  • The coefficient of static frictionis equal to or greater than the coefficient of kinetic friction.
02

Determination of coefficient of friction using position vs. time

  • We have to set up an experiment for a block sliding on a table to measure the force of friction.
  • We have to start with some initial velocity, showing down, and coming to rest to measure a moving distance L
  • We have to draw the friction force F , on the y - axis , and Normal Force N on the x - axis .
  • The slope of that graph will indicate the coefficient of kinetic friction.
  • We have to find the + y component perpendicular to the slope and + x down the slope by using a coordinate system.
  • Then apply Newton鈥檚 second law.
  • The tangent of the angle where the object slides, is knowns as the coefficient of static friction.
  • Sliding friction does not have the same variables, so it is independent of the speed of the sliding.
  • Sliding friction depends upon the material and the weight of the object.

Hence, using the above method the coefficient of friction is determined by using a position vs. time graph which is essentially independent of the speed of sliding.

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Most popular questions from this chapter

Young鈥檚 modulus for aluminum is 6.2脳1010N/m2. The density of aluminum is 2.7g/cm3, and the mass of one mole (6.02脳1023atoms)is 27g. If we model the interactions of neighbouring aluminum atoms as though they were connected by spring, determine the approximate spring constant of such a spring. Repeat this analysis for lead is: Young鈥檚 modulus for Lead 1.6脳1010N/m2and the density of lead is 11.4g/cm3, and the mass of one mole is 207g. Make a note of these results, which we will use for various purposes later on. Note that aluminum is a rather stiff material, whereas lead is quite soft.

The period of a particular spring-mass oscillator is 1 when the amplitude is5cm . (a) what would be the period if we doubled the mass? (b) What would be the period if we replaced the original spring with a spring that is twice as stiff (keeping the original mass)? (c) What would be the period if we cut the original spring in half and use just one of the pieces (keeping the original mass)? (d) What would be the period if we increased the amplitude of the original system to10cm , so that the total distance traveled in one period is twice as large? (e) What would be the period if we took the original system to a massive planet whereg=25N/kg ?

A spring suspended vertically is 18cmlong. When you suspend a 30g weight from the spring, at rest, the spring is 22cm long. Next you pull down on the weight so the spring is 23cm long and you release the weight from rest. What is the period of oscillation?

certain coiled wire with uneven windings has the property that to stretch it an amount s from its relaxed length requires a force that is given by, F=bs3so its behaviour is different from a normal spring. You suspend this device vertically, and its unstretched length is 25 cm. (a) You hang a mass of 18 g from the device, and you observe that the length is now 29 cm. What is b, including units? (b) Which of the following were needed in your analysis in part (a)? (1) The Momentum Principle, (2) The fact that the gravitational force acting on an object near the Earth鈥檚 surface is approximately mg, (3) The force law for an ordinary spring (F=kss), (4) The rate of change of momentum being zero (c) Next you take hold of the hanging 18 g mass and throw it straight downward, releasing it when the length of the device is 33 cm and the speed of the mass is 5 m/s. After a very short time, 0.0001 s later, what is the stretch of the device, and what was the change in the speed of the mass (including the correct sign of the change) during this short time interval? It helps enormously to draw a diagram showing the forces that act on the mass after it leaves your hand.

It was found that a 20gmass hanging from a particular spring had an oscillation period of 1.2s. (a) When two 20gmasses are hung from this spring, what would you predict for the period in seconds? Explain briefly.


Figure 4.58

(b) When one 20gmass is supported by two of these vertical, parallel springs (Figure 4.58), what would you predict for the period in seconds? Explain briefly. (c) Suppose that you cut one spring into two equal lengths, and you hang one 20gmass from this half spring. What would you predict for the period in seconds? Explain briefly. (d) Suppose that you take a single (full-length) spring and a single 20gmass to the Moon and watch the system oscillate vertically there. Will the period you observe on the Moon be longer, shorter, or the same as the period you measured on Earth? (The gravitational field strength on the Moon is about one-sixth that on the Earth.) Explain briefly.
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