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Chapter 5: Problem 16

A woman has a mass of \(55.0 \mathrm{kg}\). a. What is her weight on earth? b. What are her mass and her weight on the moon, where \(g=1.62 \mathrm{m} / \mathrm{s}^{2} ?\)

Short Answer

Expert verified
a. The weight of the woman on Earth is \(539 \, \mathrm{N}\). \nb. The weight of the woman on the moon is \(89.1 \, \mathrm{N}\), and her mass remains the same as on Earth, \(55.0 \, \mathrm{kg}\).

Step by step solution

01

Calculate the weight on Earth

The weight of an object on Earth can be calculated using the formula: \( \mathrm{Weight}= \mathrm{Mass} \times g\), where \( g = 9.8 \, \mathrm{m} / \mathrm{s}^{2}\) (the acceleration due to gravity). The woman's mass is given as \(55.0 \, \mathrm{kg}\). So her weight on Earth would be \(55.0 \, \mathrm{kg} \times 9.8 \, \mathrm{m} / \mathrm{s}^{2} = 539 \, \mathrm{N}\).
02

Calculate the weight on the Moon

The weight of an object on the moon can be calculated in the same way as on Earth, except we use the lunar gravity (\(1.62 \, \mathrm{m} / \mathrm{s}^{2}\)) instead of \( g = 9.8 \, \mathrm{m} / \mathrm{s}^{2}\). So the woman's weight on the moon would be \(55.0 \, \mathrm{kg} \times 1.62 \, \mathrm{m} / \mathrm{s}^{2} = 89.1 \, \mathrm{N}\).
03

Identify the mass on the moon

Mass is a scalar quantity and it does not change regardless of location. So, the mass of the woman on the moon is the same as her mass on Earth, that is, \( 55.0 \, \mathrm{kg} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Weight calculation
Calculating weight is an interesting task because it changes depending on where you are in the universe. Weight and mass are not the same, though they are often confused. To calculate weight, we can use the formula:
  • Weight = Mass \( \times \) Gravity
Where weight is measured in newtons (N), mass in kilograms (kg), and gravity in meters per second squared (m/s虏).

For example, on Earth, gravity is approximately \(9.8 \text{ m/s}^2\). So, if a person has a mass of \(55.0\) kg, their weight on Earth can be calculated using the formula:
  • Weight = \(55.0 \text{ kg} \times 9.8 \text{ m/s}^2 = 539 \text{ N}\)
This means that this person would weigh 539 newtons on Earth.
Mass and weight differences
It's essential to understand the difference between mass and weight. Mass is a measure of the amount of matter in an object and is measured in kilograms (kg). It stays the same regardless of location. Weight, however, depends on gravitational force and can vary depending on where you are in the universe.

On Earth, you might weigh more than on the Moon due to the difference in gravitational pull. But, your mass remains unchanged. For example, if you have a mass of 55 kg on Earth, you will have the same mass of 55 kg on the Moon.
  • Mass is constant.
  • Weight varies with gravity.
Gravitational force
Gravitational force is the force that attracts two bodies towards each other. It is determined by the mass of the bodies and the distance between them. However, when we're standing on a planet like Earth, we mainly feel the gravitational force that the planet exerts on us.

Earth's gravitational force is what gives us weight. The acceleration due to gravity on Earth is \(9.8 \text{ m/s}^2\). On the Moon, this gravitational force is much weaker, only about \(1.62 \text{ m/s}^2\).

Thus, when you are on the Moon, you weigh less because the gravitational force is weaker. However, your mass remains the same, which is an important distinction in understanding how gravitational force impacts your weight.
  • Stronger gravitational pull = greater weight.
  • Weaker gravitational pull = less weight.
This is why astronauts on the Moon can jump higher and carry heavier loads with ease compared to Earth, given the reduction in weight due to the lower gravitational force.

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Most popular questions from this chapter

\(\mathrm{A} 50 \mathrm{kg}\) box hangs from a rope. What is the tension in the rope if a. The box is at rest? b. The box has \(v_{y}=5.0 \mathrm{m} / \mathrm{s}\) and is speeding up at \(5.0 \mathrm{m} / \mathrm{s}^{2} ?\)

Your forehead can withstand a force of about \(6.0 \mathrm{kN}\) before fracturing, while your cheekbone can only withstand about \(1.3 \mathrm{kN}\). a. If a 140 g baseball strikes your head at \(30 \mathrm{m} / \mathrm{s}\) and stops in \(0.0015 \mathrm{s},\) what is the magnitude of the ball's acceleration? b. What is the magnitude of the force that stops the baseball? c. What force does the baseball apply to your head? Explain. d. Are you in danger of a fracture if the ball hits you in the forehead? In the cheek?

A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob's rope pulls to the left, \(15^{\circ}\) below horizontal, with \(500 \mathrm{N}\) of tension. Ellen's rope pulls toward the right, \(25^{\circ}\) below horizontal. a. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed? b. What is the tension in the vertical main cable supporting the piano?

Dana loads luggage into an airplane using a conveyor belt tilted at an angle of \(20^{\circ} .\) She places a few pieces of luggage on the belt before it starts to move, then she turns the belt on. It takes the belt \(0.70 \mathrm{s}\) to reach its top speed of \(1.2 \mathrm{m} / \mathrm{s}\). Does the luggage slip? Assume \(\mu_{\mathrm{s}}=0.50\) between the luggage and the belt.

In the winter sport of curling, two teams alternate sliding \(20 \mathrm{kg}\) stones on an icy surface in an attempt to end up with the stone closest to the center of a target painted on the ice. During one turn, a player releases a stone that travels \(27.9 \mathrm{m}\) before coming to rest. The friction force acting on the stone is \(2.0 \mathrm{N}\). What was the speed of the stone when the player released it?
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