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Chapter 4: Problem 19

Astro Why would it be easier to lift a truck on the Moon's surface than it is on Earth? SSM

Short Answer

Expert verified
The truck would be easier to lift on the Moon because its weight would be much less due to the Moon's lower gravity. On Earth the truck weighs 19600 N, while on the Moon it only weighs 3200 N.

Step by step solution

01

Identify the Variables

Here, the variable to consider is the strength of gravity. On Earth, the strength of gravity is approximately 9.8 m/s\(^2\) while on the moon it is approximately 1.6 m/s\(^2\).
02

Calculate the Weight on Earth

Using the formula for weight, which is mass multiplied by the strength of gravity (W = m*g), calculate how much the truck would weigh on earth. Let's assume the mass of the truck (m) is 2000 kg. Therefore, the weight of the truck on Earth would be W = m*g = 2000 kg * 9.8 m/s\(^2\) = 19600 N.
03

Calculate the Weight on the Moon

To calculate the weight of the same truck on the moon, use the same formula (W = m*g), but use the moon's gravitational strength. So, W = m*g = 2000 kg * 1.6 m/s\(^2\) = 3200 N.

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Key Concepts

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

Moon
The Moon is Earth's closest celestial neighbor and our natural satellite. It influences many phenomena on Earth, such as tides and even some aspects of wildlife behavior. However, one of the Moon's most fascinating aspects is its weaker gravitational pull compared to Earth. While Earth's gravity is approximately 9.8 m/s虏, on the Moon, it is about 1.6 m/s虏, which is nearly one-sixth of Earth's. This significant difference in gravity affects how objects behave on the Moon's surface. For example, if you were to visit the Moon, you would weigh much less than you do on Earth. This is why astronauts appear to float and move with ease during space missions filmed on the Moon.
Weight Calculation
Calculating weight is an essential part of understanding how gravity works on different celestial bodies. Weight is defined as the force exerted on an object due to gravity, and it's calculated using the formula \[ W = m imes g \]where
  • \( W \) is the weight of the object,
  • \( m \) is the mass of the object, and
  • \( g \) is the gravitational pull of the celestial body.
On Earth, if you have an object with a mass of 2000 kg, the weight can be calculated by multiplying the mass by Earth's gravitational force, so it would weigh 19600 N (newtons). Similarly, on the Moon, the same object would weigh much less, about 3200 N, because the Moon's gravitational force is weaker. This calculation shows why lifting heavy objects, like a truck, would be more manageable on the Moon compared to Earth.
Gravitational Force
Gravitational force is a fundamental force of nature that attracts two objects with mass towards each other. This force is what keeps planets in orbit around stars, and moons around planets. The strength of the gravitational force depends on two main factors:
  • The masses of the objects involved.
  • The distance between the centers of the two objects.
The formula to calculate gravitational force is known as Newton's law of universal gravitation:\[ F = G \frac{m_1 m_2}{r^2} \]where
  • \( F \) is the gravitational force between two objects,
  • \( G \) is the gravitational constant, approximately \( 6.674 imes 10^{-11} Nm^2/kg^2 \),
  • \( m_1 \) and \( m_2 \) are the masses of the objects, and
  • \( r \) is the distance between the centers of the two masses.
On the Moon, the gravitational force is a fraction of what it is on Earth, explaining why objects weigh significantly less there. The lighter weight makes tasks such as lifting objects easier on the Moon, which is a direct result of its lower gravitational force.

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Most popular questions from this chapter

Draw a free-body diagram for a bicycle rolling down a hill. Ignore the friction between the bicycle wheels and the hill, but consider any air resistance.

Draw a free-body diagram for a heavy crate being lowered by a steel cable straight down at a constant speed.

'The mass of an object changes with time according to \(m(t)=m_{0} e^{-b t}\), where \(m_{0}\) is the initial mass and \(b\) is a proportionality constant with units of \(s^{-1}\). The velocity of the object also changes with time, according to \(v(t)=a t+v_{0}\), where \(v_{0}\) is the initial velocity and \(a\) is the object's constant acceleration. (a) Determine an expression for the force on the object at any time \(t\). (b) Determine the force when \(m_{0}=2 \mathrm{~kg}, b=0.16 \mathrm{~s}^{-1}\), \(v_{0}=1 \mathrm{~m} / \mathrm{s}, a=6 \mathrm{~m} / \mathrm{s}^{2}\), and \(t=3 \mathrm{~s}\).

What is the net force on an apple that weighs \(3.5 \mathrm{~N}\) when you hold it at rest in your hand?

Draw a free-body diagram for a person pushing a box across a smooth floor at a steadily increasing speed. Ignore the friction between the box and the smooth floor. SSM
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