A woman at an airport is towing her 27.0 kg suitcase at constant speed by pulling on the strap at an angle θ above the horizontal. She pulls on the strap with a 32.0 N force, and the friction force on the suitcase is 11.0 N.
(a) What angle does the strap make with the horizontal?
(b) What normal force does the ground exert on the suitcase?
Draw the force diagram: 11N horizontal, and 32cosTheta horizonal. Set them equal, solve for theta.
26
adfasdfasdfasdf
To solve this problem, we can use Newton's second law and analyze the forces acting on the suitcase.
(a) To find the angle θ that the strap makes with the horizontal, we need to consider the vertical and horizontal components of the forces acting on the suitcase.
Let's break down the forces:
1. The force she applies by pulling on the strap has both a vertical and a horizontal component.
The vertical component, Fv, is given by Fv = F * sin(θ), where F is the force she applies (32.0 N) and θ is the angle of the strap above the horizontal.
The horizontal component, Fh, is given by Fh = F * cos(θ).
2. The friction force acting on the suitcase is opposing its motion and has a magnitude of 11.0 N.
Now, since the suitcase is moving at a constant speed, the net force along both the vertical and horizontal directions must be zero.
In the vertical direction, the forces are the vertical component of the pulling force (Fv) and the normal force (N) exerted by the ground. They are in opposite directions, so their sum is zero.
Therefore, Fv + N = 0.
In the horizontal direction, the only force is the horizontal component of the pulling force (Fh), which is balanced by the friction force (Fr).
Therefore, Fh - Fr = 0.
Substituting the values Fv = F * sin(θ) and Fh = F * cos(θ), and solving the equations, we can find the angle θ:
F * sin(θ) + N = 0
F * cos(θ) - Fr = 0
(b) To find the normal force exerted by the ground on the suitcase, we can simply solve for N using the equation F * sin(θ) + N = 0.
Now, let's go ahead and calculate the answers:
Given values:
F = 32.0 N
Fr = 11.0 N
(a) To find the angle θ:
F * sin(θ) + N = 0
32.0 * sin(θ) + N = 0
From this equation, we can solve for θ.
(b) To find the normal force N:
F * sin(θ) + N = 0
32.0 * sin(θ) + N = 0
Solving this equation will give us the value of N.