A woman at an airport is pulling her 19.0 kg by a strap at an angle of 32 ° above the horizontal as shown in figure Fig. P5.44. She pulls on the strap with a 40.0 N force, and friction is negligible.
(a) What is the acceleration of the suitcase?
(b) What normal force does the ground exert on the suitcase?
figure the vertical and horizontal components of the pulling force.
a=horizonalcomponentpulling force/mass
normal force=mg-verticalcomponentforce
To find the acceleration of the suitcase, we need to analyze the forces acting on it and apply Newton's second law of motion, which states: the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's break down the problem into components:
- Vertical component: Since the strap is pulled at an angle of 32° above the horizontal, the vertical component of the force is Fv = 40.0 N * sin(32°).
- Horizontal component: The horizontal component of the force is Fh = 40.0 N * cos(32°).
(a) The acceleration of the suitcase can be determined by dividing the net force acting on it by its mass:
- Net force in the vertical direction: Fv - weight = Fv - mg, where m is the mass of the suitcase (19.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Net force in the horizontal direction: Fh.
Using the vertical component, the net force in the vertical direction is:
Fv - mg = Fv - (19.0 kg * 9.8 m/s^2).
Using the horizontal component, the net force in the horizontal direction is:
Fh = Fh.
The net force acting on the suitcase is the vector sum of the net forces in the vertical and horizontal directions:
Net force = sqrt((Fv - mg)^2 + Fh^2).
The acceleration of the suitcase is then:
acceleration = Net force / mass (19.0 kg).
(b) The normal force exerted by the ground on the suitcase is equal in magnitude and opposite in direction to the vertical component of the force:
Normal force = -Fv.
To conclude, to find the answers to the given questions:
(a) Calculate the net force in the vertical and horizontal directions, and then determine the acceleration of the suitcase.
(b) Determine the normal force by considering the direction of the vertical component force.