A 7.6 kg chair is pushed across a frictionless floor with a force of 42 N that is applied at an angle of 22° downward from the horizontal. What is the magnitude of the acceleration of the chair?
F = MA, right? Just mix in a cos Θ to calculate effective force (42N x cos 22° = 38.94172N), and solve.
38.94172 = 7.6A
A = 38.94172 / 7.6
A = 5.123911m/s^2
a = F_x/m
F_x is the x-component of F, 42 cos22 = 38.94 N
AnnHiro is correct. Thanks for helping us out, Ann.
The answer should only be quoted to two significant figures, 5.1 m/s^2. The input numbers have comparable accuracy.
To find the magnitude of the acceleration of the chair, we need to resolve the applied force into horizontal and vertical components.
The vertical component of the force can be found using the formula: Fy = F * sin(θ)
where F is the magnitude of the force and θ is the angle of the force with respect to the horizontal.
Fy = 42 N * sin(22°) = 15.67 N
Since there is no vertical force acting on the chair, the vertical component of the force does not contribute to the acceleration.
The horizontal component of the force can be found using the formula: Fx = F * cos(θ)
where F is the magnitude of the force and θ is the angle of the force with respect to the horizontal.
Fx = 42 N * cos(22°) = 38.08 N
Now we can apply Newton's second law of motion to find the acceleration of the chair.
Newton's second law states: F = m * a
where F is the net force, m is the mass of the chair, and a is the acceleration.
In this case, the net force is equal to the horizontal component of the applied force: F = Fx
Rearranging the equation, we have: a = Fx / m
a = 38.08 N / 7.6 kg = 5 m/s²
The magnitude of the acceleration of the chair is 5 m/s².
To find the magnitude of the acceleration of the chair, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The formula for calculating acceleration is:
acceleration = net force / mass
In this case, the net force is the force applied to the chair, which is 42 N, and the mass of the chair is 7.6 kg.
However, the force is given at an angle with respect to the horizontal, so we need to determine the horizontal component of the force. The horizontal component is given by:
horizontal force = force * cos(angle)
Substituting the given values, the horizontal force is:
horizontal force = 42 N * cos(22°)
Now we can calculate the acceleration:
acceleration = horizontal force / mass
Substituting the horizontal force and the mass into the formula:
acceleration = (42 N * cos(22°)) / 7.6 kg
To get the final answer, calculate the expression on the right-hand side of the equation using a calculator.