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Chapter 4: Q22. (page 99)

What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.

Short Answer

Expert verified

The obtained reading on the bathroom scale is Wcos胃.

Step by step solution

01

Step 1. Measurement of Weight

Weight is expressed as the term that indicates the quantity of force applied on a particular component due to an acceleration field. In the SI system, weight is measured in the units of Newton.

The relation of the weight of a person is given by:

W=mg

Here, m is the mass and g is the gravitational acceleration.

02

Step 2. Determine the reading of weight on the bathroom scale

Consider that your weight is W and the angle made by the inclined plane is 胃. In this case, while measuring the weight of the body on an inclined plane, the bathroom scale will read the magnitude of the normal force acting between you and the plane, which is Wcos胃.

Thus, Wcos胃is the reading of your weight.

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Most popular questions from this chapter

The crate shown in Fig. 4鈥�60 lies on a plane tilted at an angle 胃=25.0oto the horizontal, with 渭k=0.19. (a) Determine the acceleration of the crate as it slides down the plane. (b) If the crate starts from rest 8.15 m up along the plane from its base, what will be the crate鈥檚 speed when it reaches the bottom of the incline?

FIGURE 4鈥�60 Crate on inclined plane. Problems 59 and 60

A 1280 kg car pulls a 350-kg trailer. The car exerts a horizontal force of3.6脳103Nagainst the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.

How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface ata=1.20m/s2.

Question: (II) The block shown in Fig. 4鈥�59 has massm=7.0kgand lies on a fixed, smooth, frictionless plane tilted at an angle of胃=22.0掳to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest at 12.0 m above the plane from its base, what will be the block's speed when it reaches the bottom of the incline?

Figure 4鈥�53 shows a block (mass mA) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block (mB), which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton鈥檚 second law to find the formulas for the acceleration of the system and the tension in the cord. Ignore the friction and the masses of the pulley and the cord.

FIGURE 4-53 Problems 32 and 33. Mass mA rests on a smooth horizontal surface; mB hangs vertically.
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