A woman at an airport is pulling her 25.0 kg by a strap at an angle of 25 ° above the horizontal as shown in figure Fig. P5.44. She pulls on the strap with a 45.0 N force, and friction is negligible.
What is the acceleration of the suitcase?
___m/s^2
(45N(cos25°))/25N= 1.63m/s^2
To find the acceleration of the suitcase, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of the object's mass and its acceleration.
Step 1: Resolve the force into its horizontal and vertical components.
In this case, the force being applied to the suitcase is at an angle of 25 degrees above the horizontal. We need to find the horizontal and vertical components of this force.
The horizontal component of the force can be calculated using the equation:
F_horizontal = F * cos(theta)
where F is the magnitude of the force (45.0 N) and theta is the angle (25 degrees).
Substituting in the given values:
F_horizontal = 45.0 N * cos(25 degrees)
Step 2: Calculate the vertical component of the force.
The vertical component of the force can be calculated using the equation:
F_vertical = F * sin(theta)
where F is the magnitude of the force (45.0 N) and theta is the angle (25 degrees).
Substituting in the given values:
F_vertical = 45.0 N * sin(25 degrees)
Step 3: Calculate the net force in the horizontal direction.
Since there is no friction, the horizontal component of the force is the only force acting in the horizontal direction.
The net force acting in the horizontal direction is given by:
F_net_horizontal = F_horizontal
Step 4: Calculate the acceleration in the horizontal direction.
To find the acceleration in the horizontal direction, we divide the net force in the horizontal direction by the mass of the suitcase.
The equation for acceleration is:
a_horizontal = F_net_horizontal / mass
Substituting in the given values:
a_horizontal = F_net_horizontal / 25.0 kg
Step 5: Solve for the acceleration.
Substitute the value of F_net_horizontal and solve:
a_horizontal = F_horizontal / 25.0 kg
At this point, you can substitute the value of F_horizontal into the equation to find the acceleration in the horizontal direction.