Physics, 05.07.2021 19:20 amoauya

A 6.00-kg block starts from rest and slides down a frictionless incline. When the block has slid a distance 2.00 m, its speed is 3.00 m/s. At what angle above horizontal is the inclined plane tilted?

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Answer from: SmokeyRN

The angle above horizontal is 13.3°.

Explanation:

The angle can be calculated with Newton's third law:

$\Sigma F = ma$

Where:

ΣF: is the forces acting on the object

m: is the mass of the object = 6.00 kg

a: is the acceleration of the object

The only force acting on the object is the weight since there is no friction, so:

$mgsin(\theta) = ma$

$gsin(\theta) = a$ (1)

Where:

θ: is the angle

g: is the acceleration due to gravity = 9.81 m/s²

We can find the acceleration from the following kinematic equation:

$v_{f}^{2} = v_{0}^{2} + 2ad$

Where:

$v_{f}$ : is the final speed = 3.00 m/s

$v_{0}$ : is the initial speed = 0 (the block starts from rest)

d: is the distance traveled = 2.00 m

The acceleration is:

$a = \frac{v_{f}^{2}}{2d} = \frac{(3.00 m/s)^{2}}{2*2.00 m} = 2.25 m/s^{2}$

Finally, the angle is (equation 1):

$\theta = sin^{-1}(\frac{a}{g}) = sin^{-1}(\frac{2.25 m/s^{2}}{9.81 m/s^{2}}) = 13.3$

Therefore, the angle above horizontal is 13.3°.

I hope it helps you!

Answer from: Quest

what was the answer?

Answer from: Quest

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

$_a^z\textrm{x}\rightarrow _{a-2}^{z-4}+_2^4\alpha$

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

$_a^z\textrm{x}+_{-1}^0\textrm{e}\rightarrow _{z-1}^a\textrm{y}$

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases $\gamma -radiations$ . this process does not change the mass number.

$_a^z\textrm{x}^*\rightarrow _a^z\textrm{x}+_0^0\gamma$

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as $\beta ^+$ -decay. in this the mass number remains same.

$_a^z\textrm{x}\rightarrow _{z-1}^a\textrm{y}+_{+1}^0e$

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

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