A m1 = 6.0 kg block on a 36.87degree incline is attached by a light rope passing

Question

A m1 = 6.0 kg block on a 36.87degree incline is attached by a light rope passing over a light, frictionless pulley to a m2 = 9.0 kg block oriented vertically as shown. The 6.0 kg block is also attached to an initially unstretched spring (with a stiffness of 30 N/m). There is friction between the 6.0 kg block and the incline with kinetic and static coefficients of 1/4 and 1/3 respectively. The system is released from rest and m2 falls. Note: sin(36.87degree) 0.60, cos(36.87) 0.80 and g = 10 m/s2. Draw FBD and KD's for both blocks after the system has started moving. Determine the acceleration of the blocks and the tension in the rope at the instant the 9.0 kg block has fallen by 0.40 m. Why can't you use the acceleration from b) and constant acceleration kinematics to determine the speed of the blocks? What is the largest mass m2, max that can be hung (instead of the 9.0 kg mass) so that the system does not move? (Hint for e: ignore the spring since it remains unstretched if neither block moves. The answer is less than 9.0 kg.)

Explanation / Answer

b)

F = (m1+m2) a

m2 g - k x - fk - m1 g sin = (m1+m2) a

m2 g - k x - k m1 g cos - m1 g sin = (m1+m2) a

9*10 - 30*0.40 - (1/4)*6*10*0.8 - 6*10*0.6 = (9+6)*a

>>> a = 2 m/s2

c)

Because the spring force is not constant and varies, therefore the acceleration is not constant and we can not use constant acceleration kinematics.

d)

e)

F = 0

m2 g - fs,max - m1 g sin = 0

m2 g - s m1 g cos - m1 g sin = 0

>>>> m2 = s m1 cos + m1 sin

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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