pertain to the following scenario: A 2.5kg block is initially released from rest
ID: 1567297 • Letter: P
Question
pertain to the following scenario: A 2.5kg block is initially released from rest at the top of a 30 degree incline as shown in the figure below. The block slides 8.0m down along the incline (which has a coefficient of kinetic friction mu_k = 0.2) before sliding an additional across a horizontal surface and compressing a spring by 30 cm. (he block is momentarily at rest the spring is compressed by 30cm.) What is the spring constant, k, of the spring? (Round to the nearest 10N/m) a.) 1420N/m b) 1110N/m c.) 1370N/m d.) 1250N/m e.) none of these Which of the following statements about the block's motion is true? a.) All of the statements listed below are false. b.) The kinetic energy the block possesses after sliding down the incline will be equal to the gravitational potential energy it initially had at the top of the incline. c.) The potential transferred to (stored in) the spring once the block reaches it will be equal to the gravitational potential energy the block initially had at the top of the incline. d.) The normal force acting on the block during its motion does positive work on the block. e.) If the incline were frictionless the block would compress the spring less than 30cm.Explanation / Answer
m = 2.5 kg, u =0 , L = 8 m, uk = 0.2
net force along vertical direction
N = mgcos(30)
Fk = uk*N
net force along hoizontal direction
mgsin(30) - Fk = ma
2.5*9.8*sin(30) - 0.2*2.5*9.8*cos(30) = 2.5*a
a = 3.2 m/s^2
from kinematic equation
v^2 - u^2 = 2as
v^2 = 2*3.2*8
v = 7.16 m/s
from conservation of energy
0.5mv^2 = 0.5kx^2
2.5*7.16^2 = k*0.3^2
k =1420 N/m
correct option is (a)
2.5*7.16^2 - 2*2.5*3.2*4= k*0.3^2
15) a) False
b) True
c) False
(d) False
(e) True
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