A 120-kg roller coaster cart is being tested on a new track, and a crash-test dummy is loaded into it. The roller coaster starts from rest at point A which is 35 m above the ground. The cart is observed to roll down the track to point B, which is 10 m above the ground. In your own words, what physics ideas would you be able to use to predict how fast the cart is moving at point B? What calculations would you use, what things would you be measuring, and what physics principles or laws would you use to make this calculation?

v₂ = 22.13 m/s

We need to measure heights of both points and the law of conservation of energy is applied to measure this speed.

Explanation:

In order to find the speed at the point B, we will use the Law of conservation of energy between points A and B to get the required results, as follows:

Total Energy of Cart at Point A = Total Energy of Cart Point B

K.E at A + P.E at A = K.E at B + P.E at B

(1/2)mv₁² + mgh₁ = (1/2)mv₂² + mgh²

(1/2)m(v₁² - v₂²) = mg(h₂ - h₁)

(1/2)(v₁² - v₂²) = g(h₂ - h₁)

where,

v₁ = velocity of cart at Point A = 0 m/s

v₂ = Velocity of Cart at Point B = ?

h₁ = height of point A relative to the ground = 35 m

h₂ = height of point B relative to the ground = 10 m

g = 9.8 m/s²

Therefore,

(1/2)[(0 m/s)² - v₂²] = (9.8 m/s²)(10 m - 35m)

- v₂² = - (2)(245 m²/s²)

v₂ = √(490 m²/s²)

v₂ = 22.13 m/s

We need to measure heights of both points and the law of conservation of energy is applied to measure this speed.

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.

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.

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 . this process does not change the mass number.

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 -decay. in this the mass number remains same.

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