A 232-g block is pressed against a spring of force constant 1.27 kN/m until the block compresses the spring 10. cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block (b) if the coefficient of kinetic friction is 0.460

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Chapter7: Conservation Of Energy
Section: Chapter Questions
Problem 23P
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8.8

We consider gravitational energy, elastic energy, kinetic energy, and internal energy. The spring is initially
compressed by x₁ = 0.100 m. The block travels up the ramp a distance d. The work that the spring does on the
block is given by the following equation.
2
2
2
W₁ = 1⁄2kx, ² - 1 1⁄2kx² ² = 1⁄2kx₁²
1
= = kx₁²2.
2
Gravity does work on the block specified in the equation below. There is no friction.
W₁
=
=
mgd cos 90° + 60
mgd sin 60
(a) Since we know W + W = 0, and
S
g
Σ
½kx² - mgd sin(
and substitution gives
7/(
= (
1.27
.232
60
0
Solving the above equation for
friction is
W =
ΔΚ, we have
= 0,
x 103 N/m)(.1
kg
g)(9.80 m/s² d sin 60
we find that the distance up the incline the block would travel in the absence of
m
d = 1.96
X
Your response differs from the correct answer by more than 10%. Double check your calculations. m.
Transcribed Image Text:We consider gravitational energy, elastic energy, kinetic energy, and internal energy. The spring is initially compressed by x₁ = 0.100 m. The block travels up the ramp a distance d. The work that the spring does on the block is given by the following equation. 2 2 2 W₁ = 1⁄2kx, ² - 1 1⁄2kx² ² = 1⁄2kx₁² 1 = = kx₁²2. 2 Gravity does work on the block specified in the equation below. There is no friction. W₁ = = mgd cos 90° + 60 mgd sin 60 (a) Since we know W + W = 0, and S g Σ ½kx² - mgd sin( and substitution gives 7/( = ( 1.27 .232 60 0 Solving the above equation for friction is W = ΔΚ, we have = 0, x 103 N/m)(.1 kg g)(9.80 m/s² d sin 60 we find that the distance up the incline the block would travel in the absence of m d = 1.96 X Your response differs from the correct answer by more than 10%. Double check your calculations. m.
A 232-g block is pressed against a spring of force constant 1.27 kN/m until the block compresses the spring 10.0
cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations,
determine how far up the incline the block moves from its initial position before it stops under the following
conditions.
(a) if the ramp exerts no friction force on the block
(b) if the coefficient of kinetic friction is 0.460
Transcribed Image Text:A 232-g block is pressed against a spring of force constant 1.27 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0° to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block (b) if the coefficient of kinetic friction is 0.460
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