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 48.0 N to the box and produces an acceleration of magnitude 2.20 2.20 m/s 2 , what is the mass of the box?

Hey, everyone. So today, we're dealing with the problem regarding the forces acting upon an object. So we're being told that we have a block of wood that is on ice. Now, this ice surface can be approximated to be a horizontal, frictionless surface, meaning no friction and it is well horizontal and a man decides to move this block of wood and applies a horizontal force of magnitude 140 newtons on the block. The block has an acceleration of 4.26 m per second. And we're being asked to determine the mass of the block. Now, this is actually pretty straightforward, but as always, let us first draw a force body diagram. So we have our IC plane, we have our box right of mass M. Now a man applies a force, a force of magnitude 140 newtons on the block. We have no friction force. So there's no opposing force in the opposite direction. But we do have a force due to weight MG which is negated by the normal force which is perpendicular and opposite or perpendicular to the surface. Uh the horizontal. In this case, the surface of motion and it'll also be MG because it prevents the block from falling into the ground, but it also prevents it from. But the weight force, the weight force, let me write that the weight force also prevents it from being shot into the air for any reason. So with all this, we can go ahead and apply this to Newton's second law. Oops which states that forces are equal to mass times acceleration, right, which means substituting in our values, we have 140 newtons is equal to mass into an acceleration of 4.26 m per second squared. This will bring us to our third step, which is just solving since we actually already have all of our values. Remember, the total force applied here is only 140 units because there's no other forces that are acting against or upon the block that will be meaningful towards the actual path to motion. The force is applied here anyways uh rearranging for the mass, which is what we're looking for will be equal to F over A which is just 1, 40 newtons divided by 4.26 m per second squared, which gives us a final answer of 32. kg or answer choice C therefore, the mass of the block is 32.9 kg. I hope this helps and I look forward to seeing you all in the next one.

6. Intro to Forces (Dynamics)

Newton's First & Second Laws

Physics

6. Intro to Forces (Dynamics)

Newton's First & Second Laws

3:08 minutes

Problem 9

Textbook Question

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: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>m</mi><mi>a</mi></math>. Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> is the force, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is the mass, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> 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: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mi>F</mi><mi>a</mi></mfrac></math>.

Step 4: Substitute the given values into the formula. Use <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>48.0</mn></math> N and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2.20</mn></math> 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.