physics stem strand

Question

LAW OF ACCELERATION 

1. A 350 kg boat is moving with a force of 30N i+ (-45N) j. (a) identify the direction of the boat.(b)What is the magnitude of the horizontal and vertical components of acceleration of the block?
2. A moving car at 20 m/s speed is accelerated to 35 m/s when it received 42 N in 35 seconds. What is the mass of the object ?

LAW OF INTERACTION

1. Two balls from opposite directions are rolling towards each other. Ball 1 and ball 2 have masses of 100g and 120g. respectively. When the two balls, they both exerted 70 N from one another. (a) What is the acceleration o each ball? (b) Identify the distance of each balls they drew from the collision in 10 seconds.

Answer 1

Problem 1.

In this problem the motion of the body with mass m = 350 kg is described as 2-dimesional, and requires use of xy -plane.

F = 30 N i - 45 N j - is a vector force with x-component F_x = 30 N and y-component F_y = - 45 N. Here i and j are unit vectors.

a) In order to find the direction of the boat with mass m = 350 kg we need to find the direction of the force, which is usually given by tan Θ of the angle Θ between x-axis and direction of the force.

Knowing that tan Θ = F_y / F_x , we obtain tan Θ = - 45 N/30 N = - 3/2 = -1.5; hence Θ is approximately 56° and vector of the force is in the IV quadrant. The direction of the boat is the same.

b) Components of the acceleration we will find using Newton's second law. a_x = F_x/m and a_y = F_y/m.

or a_x = 30N/350 kg = 0.08 m/s² a_y = - 45 N/350 kg = - 0.13 m/s²

Answer: a_x = 0.08 m/s², a_y = - 0.13 m/s²

Problem 2.

The best way to handle this problem is to use Impulse-Momentum Theorem: the total impulse of net force on a body equals the change in its linear momentum. (BTW, this is how Newton presented initially his Second Law).

Mathematically: J = Δp.

Impulse J = F_avrΔt, where J - impulse, F_avr - average force and Δt - change in time. In our case we assume that force is changing from 0 to 42 N linearly.

Change in momentum Δp = mΔv, here m - mass of the body and Δv = v_f - v_i - change in its velocity.

Now we can write:

(42/2) N x 35 s = m x (35 - 20) m/s.

Solving with respect to mass, we will get

m = 735 Ns/(15 m/s) = 49 kg

Answer: 49 kg

Problem 3. (Law of interaction)

Frankly speaking I am not 100% happy with how the problem is formulated. Ok, let's assume that this is a simple problem and we can use the Newton's second law. Then

a) acceleration a₁ = F/m₁ and acceleration a₂ = F/m₂.

or a₁ = 70 N/0.1 kg = 700 m/s² and a₂ = 70 N/0.12 kg = 583 m/s².

b) As I mentioned above, I am not happy with that part of the problem. We do not know what kind of collision the balls experienced and what was their velocities before the collisions. So sorry, but this part of the question I am unable to answer because too many scenarios are possible.

Anyway, hope that my explanation was helpful. Good luck!