Learning Goal: To practice Problem-Solving Strategy 6.1 for Newtonian mechanics

Question

Learning Goal:

To practice Problem-Solving Strategy 6.1 for Newtonian mechanics problems.

A box of mass 3.1 kg slides down a rough vertical wall. The gravitational force on the box is 30 N . When the box reaches a speed of 2.5 m/s , you start pushing on one edge of the box at a 45 angle (use degrees in your calculations throughout this problem) with a constant force of magnitude Fp = 23 N , as shown in (Figure 1) . There is now a frictional force between the box and the wall of magnitude 13 N . How fast is the box sliding 2.4 s after you started pushing on it?

Part C

*Find the box's speed vf at 2.4 s after you first started pushing on it.

Hints

Hint 1. How to approach the problem

This is a one-dimensional kinematics problem. You are given the box's initial speed and need to calculate its final speed after a certain period of time. You know that motion occurs only in the vertical direction, so there's no need to write down any equation in the x direction. All you need is ay, the y component of the box's acceleration, which can be calculated by applying Newton's second law in the y direction.

Hint 1. Find Fpy, the y component of the pushing force

Enter an expression for the y component of the pushing force, Fpy. Recall that you push on the box at a 45 angle. Use Fp for the magnitude of the pushing force.

Express your answer in terms of Fp, the magnitude of the pushing force.

Fpy =

Hint 2. Set up Newton's second law in the y direction

Newton's second law states that (Fnet)y, the y component of the net force acting on an object, is equal to the y component of the object's acceleration multiplied by its mass, that is, (Fnet)y=may.

Using the coordinate system shown in Part B, enter an expression for (Fnet)y in terms of the forces acting on the box. Use f, FG, and n for the magnitudes of the friction force, the gravitational force, and the normal force, respectively; use Fp for the magnitude of the pushing force.

Express your answer in terms of some or all of the variables f, n, FG, and Fp.

(Fnet)y=i(Fi)y= =

=may

Hint 3. Determine which kinematic equation to use

Which of the following equations is the most appropriate one to calculate the box's speed 2.4 s after you first started pushing on it?

Which of the following equations is the most appropriate one to calculate the box's speed 2.4 after you first started pushing on it?

yf=yi+viyt+12ay(t)2

vfy=viy+ayt

v2fy=v2iy+2ay(yfyi)

*vf =

m/s

Fpy =

CHo6HW PSS 6.1 Newtonian Mechanics Learning Goal: To practice Problem-Solving Strategy 6.1 for Newtonian mechanics problems. A box of mass 3.1 kg slides down a rough vertical wall. The gravitational force on the box is 30 N. When the box reaches a speed of 2.5 m/s, you start pushing on one edge of the box at a 45° angle (use degrees in your calculations throughout this problem) with a constant force of magnitude Fp 23 N, as shown in (Figure 1). There is now a frictional force between the box and the wall of magnitude 13 N. How fast is the box sliding 2.4 s after you started pushing on it? Figure 1 v l of 1 45° Type here to search

Explanation / Answer

Given that
mass = 3.1 kg
v = 2.5 m / s
Fp = 23 N
frictional = 13 N
Thita = 45 degree
gravitational force = 30 N

we know that
At the time the force is applied, t = 0

v1 = 2.5 m/s

Net force acting in y-direction,

Fnety = Weight - Fp*cos(45) - Friction

m*a = 30 - 23*cos(45) - 13

3.1*a = 0.736

a = 0.736/3.1

= 0.237 m/s^2

now Apply

v2 = v1 + a*t

= 2.5 + 0.237 * 2.4

= 3.068 m/s

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