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Chapter 4: Problem 6

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 \(\mathrm{N}\) to the box and produces an acceleration of magnitude \(3.00 \mathrm{m} / \mathrm{s}^{2},\) what is the mass of the box?

Short Answer

Expert verified
The mass of the box is 16.0 kg.

Step by step solution

01

Identify the Known Variables

We are given the force \( F = 48.0 \, \mathrm{N} \) and the acceleration \( a = 3.00 \, \mathrm{m/s^2} \).
02

Recall the Formula for Newton's Second Law of Motion

Newton's Second Law states that \( F = m \cdot a \) where \( F \) is the force applied, \( m \) is the mass of the object, and \( a \) is the acceleration.
03

Rearrange the Formula to Solve for Mass

We need to find the mass, \( m \). Rearrange the formula: \( m = \frac{F}{a} \).
04

Substitute the Known Values into the Equation

Plug in the values for force and acceleration: \( m = \frac{48.0 \, \mathrm{N}}{3.00 \, \mathrm{m/s^2}} \).
05

Calculate the Mass

Divide the force by the acceleration to get the mass: \( m = \frac{48.0}{3.00} = 16.0 \, \mathrm{kg} \).

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Key Concepts

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

Force
At the core of Newton's Second Law, force is a key concept. It is defined as the interaction that causes an object to change its velocity, effectively pushing or pulling it. Force is a vector quantity, which means it has both magnitude and direction. In the given problem, the force has a magnitude of 48.0 N and is applied horizontally.
  • The unit of force in the International System of Units (SI) is the Newton (N).
  • A force can cause an object to accelerate, decelerate, remain in motion, or change direction.
Understanding force is crucial because it explains how objects interact with one another. In many physics problems, calculating the force helps us understand the subsequent motion of objects. This problem simplifies things by assuming no friction, highlighting the direct relationship between force and motion through acceleration.
Acceleration
Acceleration measures how quickly an object's velocity changes over time. In simpler terms, acceleration tells us how fast an object is speeding up or slowing down. In our example, the acceleration is given as 3.00 m/s虏. This means that every second, the box's velocity on the frozen pond increases by 3.00 meters per second.
  • Acceleration is a vector quantity, the same as force, meaning it has both a direction and magnitude.
  • In Newton's Second Law, acceleration is directly proportional to the force exerted on the object.
  • The unit of acceleration in SI is meters per second squared (m/s虏).
In physics, understanding acceleration allows us to predict how quickly or slowly an object moves when a certain force is applied. This concept is crucial in problems related to motion, as it links force and mass together.
Mass Calculation
To find the mass of an object in scenarios governed by Newton's Second Law, we use the formula \( m = \frac{F}{a} \). This rearrangement of the law \( F = m \cdot a \) allows us to solve for mass when force and acceleration are known, as in our example.
  • Mass is a measure of the amount of matter in an object.
  • In the International System of Units, mass is measured in kilograms (kg).
  • Mass is not affected by forces like gravity, making it distinct from weight.
In our problem, calculating mass involved dividing the given force (48.0 N) by the given acceleration (3.00 m/s虏), resulting in a mass of 16.0 kg for the box. Mass calculation is foundational in physics because it helps us understand an object's resistance to acceleration when a force is applied.

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Most popular questions from this chapter

A \(\mathrm{A} 68.5 \mathrm{kg}\) skater moving initially at 2.40 \(\mathrm{m} / \mathrm{s}\) on rough horizontal ice comes to rest uniformly in 3.52 s due to friction from the ice. What force does friction exert on the skater?

A parachutist relies on air resistance (mainly on her parachute) to decrease her downward velocity. She and her parachute have a mass of 55.0 \(\mathrm{kg}\) , and at a particular moment air resistance exerts a total upward force of 620 \(\mathrm{N}\) on her and her parachute. (a) What is the weight of the parachutist? \((\mathrm{b})\) Draw a free-body diagram for the parachutist (see Section \(4.6 ) .\) Use that diagram to calculate the net force on the parachutist. Is the net force upward or downward? (c) What is the acceleration (magnitude and direction) of the parachutist?

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity, and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

(a) An ordinary flea has a mass of 210\(\mu g .\) How many newtons does it weigh? (b) The mass of a typical froghopper is 12.3 \(\mathrm{mg} .\) How many newtons does it weigh (c) A house cat typically weighs 45 \(\mathrm{N}\) . How many pounds does it weigh and what is its mass in kilograms?

A scientific instrument that weighs 85.2 \(\mathrm{N}\) on the earth weighs 32.2 \(\mathrm{N}\) at the surface of Mercury. (a) What is the acceleration due to gravity on Mercury? (b) What is the instrument's mass on earth and on Mercury?
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