Newton's laws question [grade 12]

In summary, the problem involves a child sliding down a smooth metal pole with constant acceleration and starting from rest. The child has a mass of 35.7 kg and the pole is 3.10m high. The journey to the ground takes 2.00s. The equations used for this problem are Fnet = ma and the kinematic equation for acceleration. The goal is to find the magnitude of the downward acceleration of the child and the magnitude of the upward force of friction exerted by the pole on the child. Using the given information, the downward acceleration can be calculated and then used to find the frictional force by using Fnet = ma.
  • #1
bigmac
16
0

Homework Statement



A tree house has a vertical "fire pole" of smooth metal, designed for quick exits. A child of mass 35.7 kg slides down the pole with constant acceleration, starting from rest. The pole is 3.10m high. The journey to the ground takes 2.00s.

a) what is the magnitude of the downward acceleration of the child?
b) what is the magnitude of the upward force of friction exerted by the pole on the child?

Homework Equations



Fnet = ma

The Attempt at a Solution



This is what I got so far but I have no idea on how to solve this...any pointers?

Fg = 35.7 x 9.8 = 349.86N

Umm if its constant acceleration or velocity the Fnet is 0 right?
 
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  • #2
Height of the pole is given. The time taken to slide on the pole is given. Using kinematic equation find the acceleration. Obviously it is not g, because it is not a free fall. It leads to find the frictional force.
 
  • #3

Hi there,

Firstly, great job on starting to think about the problem and attempting to solve it using the relevant equation (Fnet = ma).

To solve this problem, you will need to use Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (Fnet = ma). In this case, the net force is equal to the sum of all the forces acting on the child.

Let's break down the problem into two parts:

a) Finding the magnitude of the downward acceleration of the child.

To find the acceleration, we can use the equation d = ut + 1/2at^2, where d is the distance, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time.

In this case, the child travels a distance of 3.10m in 2.00s. Plugging in these values into the equation, we get:

3.10 = 0(2.00) + 1/2a(2.00)^2

Solving for a, we get a = 3.10/2.00^2 = 0.775 m/s^2

Therefore, the magnitude of the downward acceleration of the child is 0.775 m/s^2.

b) Finding the magnitude of the upward force of friction exerted by the pole on the child.

To find the force of friction, we can use the equation Ff = μN, where μ is the coefficient of friction and N is the normal force (which is equal to the weight of the child in this case).

We have already calculated the weight of the child to be 349.86N. To find the coefficient of friction, we need to use the fact that the child is sliding down the pole with constant acceleration. This means that the force of friction is equal to the net force acting on the child (Fnet = Ff).

Therefore, we can write the equation as:

Fnet = Ff = μN = μ(349.86) = 0.775(35.7)

Solving for μ, we get μ = 0.775/349.86 = 0.0022

Therefore, the magnitude of the upward force of friction exerted by the pole on the child is 0.0022(349.86) = 0.77
 

What are Newton's three laws of motion?

Newton's first law states that an object will remain at rest or in uniform motion unless acted upon by an external force. Newton's second law states that the force applied to an object is directly proportional to its mass and acceleration. Newton's third law states that for every action, there is an equal and opposite reaction.

How do Newton's laws apply to real-life situations?

Newton's laws can be applied to everyday situations such as riding a bike, throwing a ball, or driving a car. For example, when you pedal a bike, you are exerting a force on the pedals (Newton's second law). This force causes the bike to accelerate forward (Newton's first law) and the reaction force pushes you back (Newton's third law).

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is a measure of the gravitational force acting on an object. Mass is measured in kilograms (kg) and weight is measured in newtons (N).

How do Newton's laws relate to each other?

Newton's laws are interconnected and build upon each other. The first law explains the concept of inertia, which is necessary for understanding the second law. The second law is necessary for understanding the third law, which explains how forces always occur in pairs.

How are Newton's laws used in engineering and design?

Engineers and designers use Newton's laws to create and improve various technologies such as airplanes, cars, and bridges. For example, the design of a car's braking system relies on Newton's laws of motion to ensure safe and efficient stopping. Engineers also use these laws to calculate and predict the movement and forces acting on structures and machines.

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