Physics Question?

Question

A box is pulled at an angle of 37 degrees about the horizontal with a force of 50 N. The mass of the box is 40 kg and the coefficient of friction is 0.4. Calculate the quanties for the blanks below.

weight ________
F(subscript x) ___________
Normal force (W - Fsubcript y) _________
F (force of friction) __________
F(subscript net) ___________
Acceleration ___________

Please show/explain all work clearly please!

Answer 1

First construct the free-body diagram for the box using the usual Cartesian coordinate system. +x is to the right; +y is up.

Forces are

N, the vertical component of the contact force with the floor, in the +y direction.

uN, the horizontal component of the contact force with the floor (or friction force if you like), where u is the coefficient of friction, in the -x direction.

mg, the force of gravity from the Earth, straight down (that is, -y direction).

50 cos 37, the horizontal component of the 50-N pulling force, in the +x direction.

50 sin 37, the vertical component of the 50-N pulling force, in the +y direction.

There's no acceleration in the vertical dimension, so Newton's Second Law is F = ma = 0; that is, the sum of the vertical forces is exactly zero.

N + 50 sin 37 - mg = 0

Solve for N. This is also the weight of the box.

There is acceleration in the horizontal dimension:

50 cos 37 - uN = ma

Plug in N, m, and u and solve for a.