A student moves a box f books by attaching a rope to the box and pulling with a force of 90.0 N at an angle of 30.0°. The box of books has a mass of 20.0 kg and the coefficient of friction of kinetic friction between the bottom of the box and the sidewalk is 0.50
a. plan. choose the equation(s) or situation
First find the normal force Fn by applying the first condition of equilibrium in the vertical direction. ΣFy=0
Calculate the force of kinetic friction in the box.
µk=Fk/Fn
b.Apply Newton's second law along the horizintal Direction to find the acceleration of the box. Σfx=ma
c.Choose a convenient coordinate system and find the x and y components of all forces.( refer to the diagram)
d. find the y component of Fapp.
Fapp=?
e.find the x component of Fapp.
Fapp
f. Use the mass to find the force of gravity (g=9.8m/s²) acting on the box
Fg= m×g
To answer the given question, let's break it down step by step:
a. First, we need to find the normal force (Fn) by applying the first condition of equilibrium in the vertical direction (ΣFy = 0).
The normal force is equal to the weight of the box, which is the mass (20.0 kg) multiplied by the acceleration due to gravity (9.8 m/s²). Normal force (Fn) = m × g.
b. Next, we need to calculate the force of kinetic friction (Fk) acting on the box. The coefficient of kinetic friction (µk) is given as 0.50. The formula for kinetic friction is µk = Fk / Fn, where Fn is the normal force.
To find Fk, rearrange the formula: Fk = µk × Fn.
c. Choose a convenient coordinate system and find the x and y components of all forces.
Refer to the provided diagram to determine the angles of the forces involved. Decompose each force into its x and y components by multiplying the force magnitude by the cosine of its angle for the x-component, and by the sine of its angle for the y-component.
d. Now, let's find the y-component of the applied force (Fapp).
Since we know the angle (30.0°) and the force magnitude (90.0 N), we can use the sine function to calculate the y-component.
Fapp_y = Fapp × sin(angle)
e. Find the x-component of the applied force (Fapp).
Using the same logic as in the previous step, we can use the cosine function to calculate the x-component.
Fapp_x = Fapp × cos(angle)
f. Use the mass to find the force of gravity acting on the box (Fg).
Gravity is given by the formula Fg = m × g, where m is the mass (20.0 kg) and g is the acceleration due to gravity (9.8 m/s²).
By following these steps, you should be able to find the answers to the given question.