A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.048.0 N to the box and produces an acceleration of magnitude 2.202.20 m/s2, what is the mass of the box?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 04: Newton's Laws of Motion

Problem 9

Chapter 4, Problem 9

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude $48.0$ N to the box and produces an acceleration of magnitude $2.20$ m/s², what is the mass of the box?

Verified step by step guidance

Step 1: Identify the given values from the problem. The horizontal force applied to the box is 48.0 N, and the acceleration produced is 2.20 m/s². The surface is frictionless, so no other forces oppose the motion.

Step 2: Recall Newton's Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:

F = m a

. Here,

F

is the force,

m

is the mass, and

a

is the acceleration.

Step 3: Rearrange the formula to solve for the mass of the box. Divide both sides of the equation by the acceleration:

m = \frac{F}{a}

Step 4: Substitute the given values into the formula. Use

F = 48.0

N and

a = 2.20

m/s².

Step 5: Perform the division to calculate the mass. The result will give the mass of the box in kilograms (kg).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In this scenario, the fisherman applies a force to the box, causing it to accelerate, allowing us to calculate the mass.

Frictionless Surface

A frictionless surface is an idealized concept where no frictional forces oppose the motion of an object. In this case, the box rests on a frozen pond, which allows it to move freely when a force is applied. This simplification means that all the applied force contributes to the acceleration of the box, making calculations straightforward.

Mass

Mass is a measure of the amount of matter in an object, typically measured in kilograms. It is a scalar quantity that does not change regardless of the object's location. In the context of this problem, knowing the mass of the box is essential for understanding how it responds to the applied force and calculating its value using the relationship defined by Newton's Second Law.

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You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. If you hold a $3.85$ -kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)? Note: Part (a) asked what does the scale read when the elevator has an upward acceleration of magnitude $2.50$ m/s².

A hockey puck with mass $0.160$ kg is at rest at the origin ( $x equals 0$ ) on the horizontal, frictionless surface of the rink. At time $t equals 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$ -axis; she continues to apply this force until $t equals 2.00$ s. What are the position and speed of the puck at $t equals 2.00$ s?

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