A passenger is pulling on the strap of a 13.5-kg suitcase with a force of 67.0 N. The strap makes an angle of 34.0° above the horizontal. A 37.8-N friction force opposes the motion (horizontal) of the suitcase. Determine the acceleration of the suitcase.
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To determine the acceleration of the suitcase, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
The given force pulling on the suitcase is 67.0 N, making an angle of 34.0° above the horizontal. We can resolve this force into its horizontal and vertical components.
The vertical component of the force is given by:
F_vertical = F * sin(θ)
where F is the applied force and θ is the angle with respect to the horizontal.
Substituting the given values:
F_vertical = 67.0 N * sin(34.0°)
The horizontal component of the force is given by:
F_horizontal = F * cos(θ)
where F is the applied force and θ is the angle with respect to the horizontal.
Substituting the given values:
F_horizontal = 67.0 N * cos(34.0°)
The vertical component of the force will counteract the gravitational force acting on the suitcase. The weight of the suitcase (mg) can be determined by multiplying its mass (13.5 kg) by the acceleration due to gravity (9.8 m/s^2).
Weight of the suitcase = m * g = 13.5 kg * 9.8 m/s^2
The net force acting in the vertical direction can be determined by:
F_net_vertical = F_vertical - weight of the suitcase
The net force acting in the horizontal direction can be determined by:
F_net_horizontal = F_horizontal - friction force
Since the acceleration is the same in both the horizontal and vertical directions, we can write the equations as:
F_net_horizontal = m * a
F_net_vertical = m * a
Substituting the given values and rearranging the equations, we can solve for acceleration:
F_horizontal - friction force = m * a
Substituting the values of F_horizontal and the friction force, we have:
67.0 N * cos(34.0°) - 37.8 N = 13.5 kg * a
Simplifying the equation and solving for a:
a = (67.0 N * cos(34.0°) - 37.8 N) / 13.5 kg
Calculating the expression will give you the acceleration of the suitcase.