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Chapter 4: Problem 22

A 2010 -kg elevator moves with an upward acceleration of $1.50 \mathrm{m} / \mathrm{s}^{2} .$ What is the force exerted by the cable on the elevator?

Short Answer

Expert verified
Answer: The force exerted by the cable on the elevator is 22716.1 N upward.

Step by step solution

01

Identify known values

We are given the mass of the elevator (m = 2010 kg) and its upward acceleration (a = 1.50 m/s虏). The gravitational acceleration (g) is approximately 9.81 m/s虏 downward.
02

Calculate gravitational force

The gravitational force (Fg) is the force of gravity acting on an object, which is equal to the mass of the object multiplied by the gravitational acceleration. In this case, the gravitational force on the elevator is: Fg = m * g Fg = 2010 kg * 9.81 m/s虏 Fg = 19701.1 N (downward)
03

Apply Newton's Second Law

According to Newton's Second law, the net force (F_net) acting on an object is equal to its mass multiplied by its acceleration: F_net = m * a In this case, the net force acting on the elevator is the difference between the force exerted by the cable (Fc) and the gravitational force (Fg): F_net = Fc - Fg (since Fg is downward, and Fc is upward) We also know that F_net = m * a, so we can substitute that in the equation: m * a = Fc - Fg
04

Solve for force exerted by the cable

Now, we can solve for the force exerted by the cable (Fc) by plugging in the known values and solving for Fc: 2010 kg * 1.50 m/s虏 = Fc - 19701.1 N 3015 N = Fc - 19701.1 N Add 19701.1 to both sides of the equation to isolate Fc: Fc = 3015 N + 19701.1 N Fc = 22716.1 N
05

Final answer

The force exerted by the cable on the elevator is 22716.1 N (upward).

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Most popular questions from this chapter

A woman who weighs \(600 \mathrm{N}\) sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs $100 \mathrm{N}\(. Each armrest exerts an upward force of \)25 \mathrm{N}$ on her arms. The seat of the chair exerts an upward force of \(500 \mathrm{N}\). (a) What force does the floor exert on her feet? (b) What force does the floor exert on the chair? (c) Consider the woman and the chair to be a single system. Draw an FBD for this system that includes all of the external forces acting on it.
On her way to visit Grandmother, Red Riding Hood sat down to rest and placed her 1.2 -kg basket of goodies beside her. A wolf came along, spotted the basket, and began to pull on the handle with a force of \(6.4 \mathrm{N}\) at an angle of \(25^{\circ}\) with respect to vertical. Red was not going to let go easily, so she pulled on the handle with a force of \(12 \mathrm{N}\). If the net force on the basket is straight up, at what angle was Red Riding Hood pulling?
Yolanda, whose mass is \(64.2 \mathrm{kg},\) is riding in an elevator that has an upward acceleration of \(2.13 \mathrm{m} / \mathrm{s}^{2} .\) What force does she exert on the floor of the elevator?
A roller coaster is towed up an incline at a steady speed of $0.50 \mathrm{m} / \mathrm{s}$ by a chain parallel to the surface of the incline. The slope is \(3.0 \%,\) which means that the elevation increases by \(3.0 \mathrm{m}\) for every \(100.0 \mathrm{m}\) of horizontal distance. The mass of the roller coaster is \(400.0 \mathrm{kg}\). Ignoring friction, what is the magnitude of the force exerted on the roller coaster by the chain?
A young South African girl has a mass of \(40.0 \mathrm{kg}.\) (a) What is her weight in newtons? (b) If she came to the United States, what would her weight be in pounds as measured on an American scale? Assume \(g=9.80 \mathrm{N} / \mathrm{kg}\) in both locations.
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