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Chapter 4: Problem 1

What force is needed to accelerate a child on a sled (total mass \(=55 \mathrm{~kg}\) ) at \(1.4 \mathrm{~m} / \mathrm{s}^{2} ?\)

Short Answer

Expert verified
The force required is 77 N.

Step by step solution

01

Understanding the problem

We need to find out the force required to accelerate a child on a sled. We have the total mass of the sled and child as well as the desired acceleration.
02

Identify the relevant formula

The formula to calculate the force needed to accelerate an object is Newton's second law of motion. This formula is: \[ F = m \cdot a \]where \(F\) is the force in newtons, \(m\) is the mass in kilograms, and \(a\) is the acceleration in meters per second squared.
03

Substitute the known values

Plug the mass \(m = 55\,\text{kg}\) and the acceleration \(a = 1.4\,\text{m/s}^2\) into the formula:\[ F = 55 \times 1.4 \]
04

Calculate the force

Now, multiply the mass by the acceleration to find the force:\[ F = 55 \times 1.4 = 77 \text{ N} \]
05

Conclusion

The force needed to accelerate the child on the sled at \(1.4\, \text{m/s}^2\) is \(77\, \text{N}\). This force is directed in the same direction as the acceleration.

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Key Concepts

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

Force Calculation
Force calculation is a fundamental aspect of Newton's Second Law of Motion. When you need to determine the force acting on an object, this law provides a straightforward approach. The formula you use for force calculation is: \[ F = m \cdot a \]where \(F\) represents the force in newtons, \(m\) the mass in kilograms, and \(a\) the acceleration in meters per second squared.
This formula shows that force is a product of mass and acceleration.
  • The greater the mass of an object, the more force you need to accelerate it.
  • Similarly, higher acceleration requires more force.
Force calculation helps bridge the physical relationship between how heavy an object is and how quickly you want it to change velocity.
Mass and Acceleration
Mass and acceleration are key components in understanding motion. Here's how:
  • Mass: It refers to the amount of matter in an object. It plays a crucial role in motion because it is resistant to changes in velocity. This resistance is known as inertia. The more mass an object has, the harder it is to move or, conversely, to stop moving.
  • Acceleration: This is the rate of change of an object's velocity over time. It indicates how quickly an object is speeding up or slowing down. In our sled example, acceleration is observed when the sled changes speed while moving forward.
Understanding mass and acceleration allows us to predict and control an object's motion in varied circumstances. When we discuss these variables within force calculation, we widthen our ability to solve real-world problems.
Physics Problem Solving
Physics problem solving involves breaking down complex ideas into manageable steps. Solving a problem like calculating force requires a logical and systematic approach. Here鈥檚 a simplified strategy:
  • Understand the problem: Recognize what you need to find. For example, in our exercise, identify that "force" is the unknown.
  • Identify relevant information: Gather all given data, such as mass \(m = 55\, \text{kg}\) and acceleration \(a = 1.4\, \text{m/s}^2\) in our example.
  • Select an appropriate formula: Using Newton's Second Law, choose \(F = m \cdot a\).
  • Substitute values: Insert the values into the equation to get your result.
  • Calculate: Perform mathematical operations to achieve the solution, calculating \[ F = 55 \times 1.4 = 77 \, \text{N} \]
  • Review and conclude: Verify the logic and numerical correctness of the results.Ensure results fit with physical understanding of the problem.
Effective physics problem solving builds your confidence to handle various scenarios by applying core principles methodically.

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Most popular questions from this chapter

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of \(920 \mathrm{kg},\) can accelerate on a level road from rest to 21 \(\mathrm{m} / \mathrm{s}\) \((75 \mathrm{km} / \mathrm{h})\) in 12.5 \(\mathrm{s} .\) Using these data, calculate the maximum steepness of a hill.

(1) A \(650-N\) force acts in a northwesterly direction. A second 650 -N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

An elevator (mass \(4850 \mathrm{~kg}\) ) is to be designed so that the maximum acceleration is \(0.0680 g .\) What are the maximum and minimum forces the motor should exert on the supporting cable?

A \(450-\mathrm{kg}\) piano is being unloaded from a truck by rolling it down a ramp inclined at \(22^{\circ} .\) There is negligible friction and the ramp is \(11.5 \mathrm{~m}\) long. Two workers slow the rate at which the piano moves by pushing with a combined force of \(1420 \mathrm{~N}\) parallel to the ramp. If the piano starts from rest, how fast is it moving at the bottom?

A person jumps from the roof of a house 3.9 -m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of \(0.70 \mathrm{~m} .\) If the mass of his torso (excluding legs) is \(42 \mathrm{~kg},\) find (a) his velocity just before his feet strike the ground, and (b) the average force exerted on his torso by his legs during deceleration.
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