Physics ('Basic' Problems)

Question

Please, help me with these problems. Also include a step-by-step procedure and a short clear explanation.

1. Two objects collide in space. The first object is twice as heavy as the second object. If the acceleration of the first object is 12.2 meter per second square, what is the acceleration of the second object?
2. How much power is required if a car needs to pull an object in an inclined road of 45 degrees using 32.5 N in 1 kilometer? Assume that the road is frictionless.
3. A particle has a mass of 1.4 x 10^(-12) kg. If it is moving at a speed of 1.5 x 10^(9) meter per second, how much kinetic energy does the particle have?

Thank you so much!

Answer 1

Problem 1.

There are two interacting objects. According to Newton's third law when two objects interact, they exert on each other forces of opposite directions and same magnitude. We know that m₁ / m₂ = 2.

We can write F₁ = F₂. And we will use the Newton's second law to express the force F = ma.

Now we have

m₁a₁ = m₂a₂

Acceleration of the second body

a₂ = (m₁ / m₂) x a₁ = 2a₁

Substituting for acceleration of the first body, we will have

a₂ = 2 x 12,2 m/s² = 24.4 m/s²

Answer: 24.4 m/s²

Problem 2.

The problem could not be solved. In order to find a power, work per unit time, we need to know the time. It is not provided.

In case of motion with constant speed v, power P = Fv, but again, we do not know the speed. and this is not a uniform motion. If unbalanced force applied to the body, acceleration is a must. So, the problem does not make any sense.

Problem 3.

In principle you can use the formula for kinetic energy K = 1/2 mv². here m - mass of the particle and v its speed. There is one big but... The speed you provided is greater than the speed of light 3 x 10 ⁸ m/s. Please check the numbers.

Best regards,

Grigoriy S.