/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 What net force must act on a 540... [FREE SOLUTION] | 91Ó°ÊÓ

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What net force must act on a 540-kg golf cart to give it an acceleration of \(2.5 \mathrm{~m} / \mathrm{s}^{2}\) ?

Short Answer

Expert verified
The net force required is 1350 N.

Step by step solution

01

Understand the Problem

We need to find the net force acting on a golf cart. We are given the mass of the golf cart, which is 540 kg, and its acceleration, which is \(2.5 \, \mathrm{m/s^2}\). We will use the formula for force based on Newton's second law of motion.
02

Apply Newton's Second Law

Newton’s second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is: \[ F = m \cdot a \]where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
03

Substitute the Values

Substitute the given values into the formula. Here, \( m = 540 \, \mathrm{kg} \) and \( a = 2.5 \, \mathrm{m/s^2} \): \[ F = 540 \, \mathrm{kg} \times 2.5 \, \mathrm{m/s^2} \]
04

Calculate the Force

Now calculate the force by performing the multiplication: \[ F = 540 \, \mathrm{kg} \times 2.5 \, \mathrm{m/s^2} = 1350 \, \mathrm{N} \]So, the net force is 1350 Newtons.

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Key Concepts

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

Net Force Calculation
Calculating net force is a fundamental aspect of understanding motion in physics. It involves determining the total force acting on an object, taking into account all forces that may be involved. In this context, the net force is the result of adding up all individual forces acting on an object. For a comprehensive calculation:
  • Identify the forces acting in the same direction as positive forces.
  • Identify forces acting in the opposite direction as negative forces.
  • Add all these forces together to get the net force.
In our exercise with the golf cart, we've used Newton’s Second Law to calculate the force required to accelerate the cart. The formula used encapsulates all these types of force into a simple equation, allowing you to quickly find out the necessary force if you know an object's mass and acceleration. Net force is crucial because it tells us how things will move.
Mass and Acceleration
Mass and acceleration are key components in Newton's Second Law. Understanding these two concepts can unlock a better understanding of motion:
  • Mass is how much matter is in an object, usually measured in kilograms (kg). It's a measure of an object's inertia - the resistance to changes in motion.
  • Acceleration refers to how quickly an object changes its velocity. It's measured in meters per second squared (\( \mathrm{m/s}^2\)).
Together, they tell us how much an object will accelerate when a given force is applied. A larger mass means that a greater force is needed for the same acceleration. Meanwhile, a smaller mass would require less force for the same level of acceleration. This relationship is core to understanding how objects move in our world.
Physics Problem Solving
Solving physics problems systematically can help you understand complex concepts more easily. Here's a concise approach to solving problems like our golf cart exercise:
  • Understand the Problem: Identify what is given and what needs to be found. Here, the mass and acceleration were provided.
  • Apply the Relevant Equations: Use known equations, such as Newton's Second Law, to relate the quantities. The formula \(F = m \cdot a\) allowed us to find the force.
  • Substitute and Solve: Fill in the known values and perform calculations to find the answer. Calculating gives us concrete results, such as \(1350 \mathrm{N}\) for the net force.
  • Check Your Work: Verify the solution to ensure it makes sense. Double-check calculations and units.
By following these steps, you can tackle and understand a wide variety of physics problems, building a solid foundation for further learning.

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Most popular questions from this chapter

A \(0.26-\mathrm{kg}\) rock is thrown vertically upward from the top of a cliff that is \(32 \mathrm{~m}\) high. When it hits the ground at the base of the cliff, the rock has a speed of \(29 \mathrm{~m} / \mathrm{s}\). Assuming that air resistance can be ignored, find (a) the initial speed of the rock and (b) the greatest height of the rock as measured from the base of the cliff.

In a tennis match a player wins a point by hitting the \(0.059-\mathrm{kg}\) ball sharply to the ground on the opponent's side of the net. If the ball bounces upward from the ground with a speed of \(16 \mathrm{~m} / \mathrm{s}\) and is caught by a fan in the stands when it has a speed of \(12 \mathrm{~m} / \mathrm{s}\), how high above the court is the fan? Ignore air resistance.

After hitting a long fly ball that goes over the right fielder's head and lands in the outfield, a batter decides to keep going past second base and try for third base. The \(62-\mathrm{kg}\) player begins sliding \(3.4 \mathrm{~m}\) from the base with a speed of \(4.5 \mathrm{~m} / \mathrm{s}\). (a) If the player comes to rest at third base, how much work was done on the player by friction with the ground? (b) What was the coefficient of kinetic friction between the player and the ground?

You push a 67-kg box across a floor, where the coefficient of kinetic friction is \(\mu_{\mathrm{k}}=0.55\). The force you exert is horizontal. How much power is needed to push the box at a speed of \(0.50 \mathrm{~m} / \mathrm{s}\) ?

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