Math Problem Statement

A 12.7 kilogram package is pulled with a 28.5 newton force at a 60.3 degree angle, across the ground where the coefficient of friction is equal to 0.0802. What is the force of friction on the package? Force equals blank newtons. Remember to indicate if the force is positive with a plus sign or negative with a minus sign.

Solution

To find the force of friction on the package, we need to calculate the frictional force using the formula:

ffriction=μNf_{\text{friction}} = \mu \cdot N

Where:

  • μ\mu is the coefficient of friction (0.0802),
  • NN is the normal force.

The normal force NN can be calculated by considering the forces acting vertically on the package. The weight of the package and the vertical component of the applied force affect the normal force. Here's the process:

  1. Weight of the package: W=mg=12.7kg9.81m/s2=124.587NW = m \cdot g = 12.7 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 124.587 \, \text{N}

  2. Vertical component of the applied force: The vertical component of the applied force FyF_y is: Fy=Fsin(θ)=28.5Nsin(60.3)F_y = F \cdot \sin(\theta) = 28.5 \, \text{N} \cdot \sin(60.3^\circ)

  3. Normal force: The normal force NN is the weight minus the vertical component of the applied force: N=WFyN = W - F_y

  4. Frictional force: Once we have NN, the frictional force can be found using ffriction=μNf_{\text{friction}} = \mu \cdot N.

Let me calculate these values.The force of friction on the package is +8.01N+8.01 \, \text{N}.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

  1. How would the force of friction change if the coefficient of friction was higher?
  2. What would happen if the angle of the applied force increased to 90 degrees?
  3. How can you calculate the horizontal component of the applied force?
  4. What is the net force acting on the package?
  5. How would the acceleration of the package be determined from the net force?

Tip: Friction always opposes the motion or attempted motion between two surfaces in contact.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Physics
Newton's Laws of Motion
Friction
Vectors

Formulas

Frictional force: f_friction = μ * N
Normal force: N = W - F_y
Weight: W = m * g
Vertical component of applied force: F_y = F * sin(θ)

Theorems

Newton's Second Law

Suitable Grade Level

Grades 10-12