Zach, whose mass is 80 kg, is in an elevator descending at 10 m/s. The elevator takes 3.0 s to brake to a stop at the first floor. What is Zach's weight before the elevator starts braking?

검증된 단계별 안내

Step 1: Understand the concept of weight. Weight is the force exerted on an object due to gravity and is calculated using the formula:

W = m g

, where

m

is the mass of the object and

g

is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

Step 2: Identify Zach's mass from the problem. His mass is given as 80 kg.

Step 3: Use the formula for weight to calculate Zach's weight before the elevator starts braking. Substitute

m = 80

kg and

g = 9.8

m/s² into the formula

W = m g

Step 4: Perform the multiplication to find Zach's weight. Multiply 80 kg by 9.8 m/s² to determine the force exerted on him due to gravity.

Step 5: Interpret the result. The calculated weight represents Zach's weight before the elevator starts braking, as it is unaffected by the elevator's motion at this point.

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주요 개념

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Weight

Weight is the force exerted on an object due to gravity, calculated as the product of mass and the acceleration due to gravity (approximately 9.81 m/s² on Earth). For Zach, whose mass is 80 kg, his weight can be determined using the formula: Weight = mass × gravity, resulting in a force measured in newtons.

Mass

Mass is a measure of the amount of matter in an object, typically measured in kilograms. It is a scalar quantity and does not change regardless of the object's location in the universe. In this scenario, Zach's mass is given as 80 kg, which is essential for calculating his weight.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates towards the Earth when in free fall, approximately 9.81 m/s². This constant is crucial for calculating weight, as it represents the gravitational pull acting on an object's mass. It remains constant near the Earth's surface, allowing for straightforward weight calculations.