Question

What is the magnitude of the acceleration a of the chair? What is the magnitude of the normal force F_N acting on the chair? Express your answers, separated by a comma, in meters per second squared and newtons to three significant figures. When solving problems involving forces and Newton's laws, the following summary of things to do will start your mind thinking about getting involved in the problem at hand. Draw a sketch of the situation. Consider only one object (at a time), and draw a free-body diagram for that body, showing all the forces acting on that body. Do not show any forces that the body exerts on other bodies. If several bodies are involved, draw a free-body diagram for each body separately, showing all the forces acting on that body. Newton's second law involves vectors, and it is usually important to resolve vectors into components. Choose an x and y axis in a way that simplifies the calculation. For each body, Newton's second law can be applied to the x and y components separately. That is the x component of the net force on that body will be related to the x component of that body's acceleration: sigma F_x = ma_x, and similarly for the y direction. Solve the equation or equations for the unknown(s). Apply these steps Use the steps outlined above to find the magnitude of the acceleration a of a chair and the magnitude of the normal force F_N acting on the chair: Yusef pushes a chair of mass m = 45.0 kg across a carpeted floor with a force F_p (the subscript 'p' here is lowercase and throughout the question) of magnitude F_p = 164 N directed at theta = 35.0 degrees below the horizontal (Figure 1). The magnitude of the kinetic frictional force between the carpet and the chair is F_k = 91.0 N.

Answer 1

To find the magnitude of the acceleration of the chair, we use Newton's second law. The equation F_net = ma allows us to solve for the acceleration. The magnitude of the normal force can be found by considering the forces in the vertical direction and setting the sum of the forces equal to zero. The normal force is equal to the weight of the object.

The magnitude of the acceleration a of the chair can be found by applying Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the horizontal component of the applied force minus the kinetic frictional force. So we have:

F_net = F_p * cos(theta) - F_k

Next, we can use the equation F_net = ma to solve for the acceleration:

a = F_net / m

The magnitude of the normal force F_N acting on the chair can be found by considering the forces in the vertical direction. Since the chair is not accelerating in the vertical direction, the sum of the forces must be zero. So we have:

F_N - mg = 0

From this, we can solve for the normal force:

F_N = mg