A box (w = 75 N) rests on an inclined plane, angled 30degree above the horizonta

Question

A box (w = 75 N) rests on an inclined plane, angled 30degree above the horizontal. The coefficient of static friction is mu_s = 0.50, and the coefficient of kinetic friction is mu_k = 0.40. You push on the box with a force F, parallel to the plane. If the box is initially at rest, what is the minimum force F that will keep it from sliding downhill? If the box is initially at rest, what is the maximum force that you can exert without moving the box? If the box is sliding, what force F will keep the box moving uphill at a constant velocity? If the box is sliding, what force F will keep the box moving downhill at a constant velocity?

Explanation / Answer

here ,

weight , W = 75 N

us = 0.50

uk = 0.40

1)

let the minimum force is F

normal reaction , N = m *g * cos(theta)

for box to stay in place

m * g * sin(theta) - us *N - F = 0

75 * sin(30) - 75 * cos(30) * 0.50 - F = 0

F = 5.032 N

the minimum force F needed is 5.032 N

2)

for the maximum force

for box to stay in place

m * g * sin(theta) - us *N - F = 0

75 * sin(30) + 75 * cos(30) * 0.50 - F = 0

F = 70 N

the maximum force F needed is 70 N

3)

for the box to move with contant velocity up the hill

m * g * sin(theta) + uk *N - F = 0

75 * sin(30) + 75 * cos(30) * 0.40 - F = 0

F = 63.5 N

the force F needed is 63.5 N

4)

for the box to move down the hill

m * g * sin(theta) - uk *N - F = 0

75 * sin(30) - 75 * cos(30) * 0.40 - F = 0

F = 11.51 N

the force F needed is 11.51 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.