A block slides on a frictionless, horizontal surface with a speed of 1.32 m/s. The block encounters an unstretched spring and co
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Answer
a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.
now, L H S
s = distance
dimension of distance = [M⁰L¹T⁰]
now, equation on the right hand side
R H S
u = speed
u = m/s
Dimension of speed = [M⁰L¹T⁻¹]
dimension of time
t = sec
Dimension of time = [M⁰L⁰T¹]
Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
now, acceleration= a
a = m /s²
dimension of acceleration = [M⁰L¹T⁻²]
dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
hence, the dimension are balanced.
so, L H S = R H S
b) Moment of inertia of hollow sphere =
Moment of inertia of solid sphere =
we know,
Torque is the force that causes rotation
If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.
Thus the solid sphere would accelerate more.
Answer: a) 110.3N b) 0.39
Explanation:
a) The normal reaction force acts in the vertical direction opposite the weight of the object(check attachment for diagram).
Since the object is inclined at 38° to the horizontal, the weight (W) will become Wcos38°.
Since the body is not moving vertically, its acceleration I'm the vertical direction will be zero.
According to newton's first law,
F = ma
Since we have two forces acting in the vertical direction, we will take their sum
R - Wcos38° = m(0)...1
Note that normal reaction (R) is acting in the positive y direction while the weight is in the negative y direction.
From 1,
R - Wcos38° = 0
R = Wcos38°
R = mg cos38°
R = 14×10×cos38°
R = 140cos38°
R = 110.3N
b) For the coefficient of friction,
Taking the sum of forces along x -direction
Fm - Ff = ma
Since a = 0(constant velocity)
Fm = Ff = 43N
Note that Fm is the moving force (force that causes the body to move)
Ff = frictional force
Since Ff = nR
n is the coefficient of friction
43 = n× 110.3
n = 43/110.3
n = 0.39
Coefficient of kinetic friction = 0.39
