Answer:
38.6 N
2.57 m/s²
Explanation:
Draw a free body diagram of the box. There are four forces:
Weight force mg pulling down,
Normal force N pushing up,
Friction force Nμ pushing left,
and applied force P pulling at an angle 40°.
Sum of forces in the y direction:
∑F = ma
N + P sin 40° − mg = 0
N = mg − P sin 40°
The net force in the x direction is:
∑F = P cos 40° − Nμ
∑F = P cos 40° − (mg − P sin 40°) μ
∑F = P cos 40° − mgμ + Pμ sin 40°
∑F = P (cos 40° + μ sin 40°) − mgμ
Plugging in values:
∑F = (80 N) (cos 40° + 0.23 sin 40°) − (15 kg) (10 m/s²) (0.23)
∑F = 38.6 N
Net force equals mass times acceleration:
∑F = ma
38.6 N = (15 kg) a
a = 2.57 m/s²
