A block with mass m 1 = 9.1 kg is on an incline with an angle = 33° with respect

Question

A block with mass m1 = 9.1 kg is on an incline with an angle = 33° with respect to the horizontal. For the first question there is no friction between the incline and the block.

1) When there is no friction, what is the magnitude of the acceleration of the block?

2) Now with friction, the acceleration is measured to be only a = 3.21 m/s2. What is the coefficient of kinetic friction between the incline and the block?

3) To keep the mass from accelerating, a spring is attached with spring constant k = 147 N/m. What is the coefficient of static friction if the spring must extend at least x = 14 cm from its unstretched length to keep the block from moving down the plane?

4) The spring is replaced with a massless rope that pulls horizontally to prevent the block from moving. You should assume that the static friction force is a maximum (the coefficient of static friction times the normal force) but notice that the presence of the rope will alter the normal force. What is the tension in the rope? You need to use the same coefficient of friction that you found in part 3 above.

5) Now a new block is attached to the first block. The new block is made of a different material and has a coefficient of static friction = 0.97. What minimum mass is needed to keep the system from accelerating?

Explanation / Answer

1> a = g sin 33

a = 5.33 m/sec2

2> a = F/m

a = [mg sin 33 - u mg cos 33]/m

a = [g sin 33 - u g cos 33]

a = 9.8*[sin 33 - u cos 33]

0.32 = 0.54 - u*0.83

u = 0.26

this will be the cofficient of kinetic friction.

3> force exerted by spring, F = kx

F = 147*0.14

F = 20.58 N

u*9.1*9.8*cos 33 = 20.58

u = 0.275

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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