Question

The average force necessary to stop a hammer with 25 NS momentum in \(0.04 \mathrm{sec}\) is \(\quad \mathrm{N}\) (A) 625 (B) 125 (C) 50 (D) 25

Short answer

The average force necessary to stop the hammer is calculated using the formula \(F = \frac{\Delta{P}}{\Delta{t}}\). Plugging in the given values, we get \(F = \frac{25 \, \mathrm{Ns}}{0.04 \, \mathrm{sec}} = 625 \, \mathrm{N}\). The correct answer is (A) 625 N.

Step-by-step solution

Write down the known values

We know the following values from the given exercise: - Momentum (P) = 25 Ns - Time (t) = 0.04 sec

Write the formula for average force

The formula for average force (F) can be expressed as the change in momentum (∆P) divided by the time interval (∆t). Mathematically, the formula can be written as: \[F = \frac{\Delta{P}}{\Delta{t}}\]

Calculate the average force

Now, plug in the known values into the formula: \[F = \frac{25 \, \mathrm{Ns}}{0.04 \, \mathrm{sec}}\] Divide 25 Ns by 0.04 sec to find the average force: \[F = 625 \, \mathrm{N}\]

Choose the correct option

The average force necessary to stop the hammer is 625 N, which corresponds to option (A). Therefore, the correct answer is: (A) 625

Key concepts

Momentum

Momentum is a fundamental concept in physics that describes the motion of an object. It is typically denoted by the letter 'P'. Momentum is the product of an object's mass and its velocity. In mathematical terms, momentum is expressed as:\[ P = m \times v \]where:

• \( P \) = Momentum
• \( m \) = Mass of the object
• \( v \) = Velocity of the object

Momentum is a vector quantity, meaning it has both a magnitude and a direction. It reflects not just how much motion an object has, but also the direction of that motion.
In the given exercise, the momentum is specified as 25 Ns, representing the hammer's motion before it is stopped.

Time Interval

The time interval is the duration over which a change occurs. In physics problems, understanding the time over which events occur is crucial for calculations. In the context of the original exercise, the time interval is noted to be 0.04 seconds. This represents the time it takes for the hammer to come to a stop.
The time interval is often denoted by \( \Delta t \) and is important when calculating average force. It helps to determine how quickly a force acts upon an object to bring about a change in motion.

Change in Momentum

Change in momentum, often denoted as \( \Delta P \), is a measure of how much an object's momentum has altered over a given time frame. This change occurs when a force acts on an object, causing it to accelerate or decelerate - in other words, an alteration in velocity.
The formula for calculating change in momentum is straightforward, as it is directly related to force and time interval.\[ F = \frac{\Delta P}{\Delta t} \]This equation illustrates the relationship between force, change in momentum, and the time interval. Applying a force over a specific time can either increase or decrease momentum, depending on the direction of the force relative to the object's motion.
In the exercise, knowing the momentum change is key in calculating the average force necessary to stop the hammer.