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Chapter 6: Q.6 (page 154)

A construction worker with a weight of 850N stands on a roof that is sloped at 20°. What is the magnitude of the normal force of the roof on the worker?

Short Answer

Expert verified

The roof's normal force on the worker is of the magnitude798.74N.

Step by step solution

01

Magnitude : 

The greatest extent of size and direction of an item is defined as magnitude.

02

Explanation : 

Weight of construction worker = 850N,

Slope of the roof = 20°.

The gymnast's free body diagram is given below,

The force equation in the roof's usual direction,

-Wcos+N=0

W= construction worker's weight,

θ= slope of the roof,

N= the roof's normal force on the worker.

Substitute 850Nfor Wand 20°for θto find N.

-850Ncos20°+N=0N=850N0.939=798.74N

Hence, the roof's normal force on the worker is of the magnitude 798.74N.

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Most popular questions from this chapter

Boxes A and B in FIGURE Q6.13 both remain at rest. Is the friction force on A larger than, smaller than, or equal to the friction force on B? Explain

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a “crumple zone” in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1mas the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton’s first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5mm. a. A 60kgperson is in a head-on collision. The car’s speed at impact is 15m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

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