a wagon is pulled at a constant speed at an angle of 46 dregress with a force of 100N. ehat is the force of friction between the wagon and the ground ?
To calculate the force of friction between the wagon and the ground, we need to use the concept of vector decomposition. Here's how you can calculate it step by step:
Step 1: Resolve the force into its horizontal and vertical components.
- The vertical component is given by Fv = F * sin(θ), where θ is the angle of 46 degrees and F is the force of 100N.
- The horizontal component is given by Fh = F * cos(θ).
Step 2: Determine the vertical forces acting on the wagon.
- In this case, we have the vertical component of the force (Fv) acting upward and the weight of the wagon acting downward. The weight can be calculated using the formula W = m * g, where m is the mass of the wagon and g is the acceleration due to gravity (approximately 9.8m/s^2).
Step 3: Equate the vertical forces.
- Since the wagon is pulled at a constant speed, there is no vertical acceleration. Therefore, the sum of the upward forces must equal the sum of the downward forces.
- This can be expressed as Fv - W = 0.
Step 4: Solve for the force of friction (Ff).
- In this case, the force of friction between the wagon and the ground acts parallel to the ground, opposing the horizontal motion.
- The force of friction can be found by using the equation Ff = Fh.
Let's calculate the force of friction:
Given:
F = 100N
θ = 46 degrees
g = 9.8m/s^2 (approximation)
Step 1:
Fv = F * sin(θ) = 100N * sin(46°) ≈ 72.13N
Fh = F * cos(θ) = 100N * cos(46°) ≈ 69.13N
Step 2:
Calculate the weight of the wagon:
W = m * g
Step 3:
Fv - W = 0
Step 4:
Since the wagon is pulled at a constant speed, there is no acceleration, and the force of friction (Ff) will be equal to Fh.
Therefore, Ff ≈ 69.13N.
So, the force of friction between the wagon and the ground is approximately 69.13N.