(20%) Problem 3: A block of mass m = 3.5 kg is attached to a spring with spring
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(20%) Problem 3: A block of mass m = 3.5 kg is attached to a spring with spring constant k= 890 Nm. It is initially at rest on an inclined plane that is at an angle of = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is ,-0.14. In the initial position, where the spring is compressed by a distance of d-0.17m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational energy of the block as zero l d I Randomized Variables m=3.5 kg k= 890 N/m d=0.17 m = 23° ,-0.14 ©theexpert ta.com 50% Part (a) what is the block's initial mechanical energy, Eo in J? 50% Part 1) If the spring pushes the block up the incline, what distance, L in meters, will the block travel before coming to rest? The spring remains attached to both the block and the fixed wall throughout its motion. Grade Summary Deductions Potential 0% 100%Explanation / Answer
Mass = m = 3.5 kg
k = 890 N/m
d = 0.17 m
k = 0.14
= 28 degree
a) block's initial mechanical energy = ½kx² = ½*890*0.17² = 12.86 J
b) The weight (force) in line with the incline = 3.5*9.8*sin28 = 16.1 N
The force of friction in line with the incline (opposing motion) = 0.14*3.5*9.8*cos28 = 4.24 N
So 12.86 J = [16.1 + 4.24]*L
L = 0.632 m
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