Discuss the concept of centripetal force in two different situations?, question help

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its about some Q about physics 1 please see file that I attach .

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1. a. Discuss the concept of centripetal force in two different situations? b. The vectors A and B are given by: A = 2i + 3j and B = – i + 2j. Determine the scalar dot product A . B. Find the angle between A and B. c. Suppose the position of a particle is given as a function of time by r(t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct2 + d, where a = 1 m/s, b = 1 m, c = 0.225 m/s2, and d = 1 m. (a) Calculate the average velocity during the time interval from t = 2 s to t = 5 s. (b) Determine the velocity and the speed at t = 3 s. 2. a. The vector position of a particle varies in time according to the equation r = 4.0i – 8.0t2j. (a) Find an expression for the velocity and acceleration of the particle as a function of time. (b) Calculate the particle’s position and velocity at t = 1.0 sec. b. A train slows down as it rounds a sharp horizontal turn, going from 100 km/h to 60.0 km/h in the 14.0 s it takes to round the bend. The radius of the circle is 160 m. Compute the total acceleration and the angle at the moment the train speed reaches 60.0 km/h. . 3. a. Discuss the concept of coefficient of friction, and provide its units b. A traffic light weighing 98 N hangs from a cable tied to two other cables fastened to a support. The upper cables make angles of 30o and 60o with the horizontal. Find the tension in the two cables. c. If an object weighing 40 N is hanging from the ceiling of an elevator, what will be the tension in the rope if the elevator is moving (a) up with an acceleration of 3.0 m/s2? (b) down with an acceleration of 4.0 m/s2? and (c) down with an acceleration of 9.8 m/s2? d. In an Atwood machine, find the acceleration of the two objects and the tension in the lightweight string. e. A hockey puck on a frozen pond is given an initial speed of 30 m/s. If the puck always remains on the ice and slides 225 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice.
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ANSWERS
1.
a) Discuss the concept of centripetal force in two different situations?
Centripetal force is defined as, “The component of a force acting on a body in curvilinear motion
that is directed toward the center of curvature or axis of rotation.” Two cases of centripetal force
application;
I.

A car going round a corner. When seated on the right close to the door, you tend to feel
as if you are being pulled outside when the car makes a left turn. What actually happens
is the door moving towards you due to the centripetal force.

II.

The swirling of a stone attached to a string. The centripetal force keeps the stone from
flying away.

b) The vectors A and B are given by: A = 2i + 3j and B = – i + 2j. Determine the scalar
dot product A . B. Find the angle between A and B.
𝐴 ∙ 𝐵 = 𝐴𝑖 ∗ 𝐵𝑖 + 𝐴𝑗 + 𝐵𝑗
𝐴 ∙ 𝐵 = (2 ∗ −1) + (3 ∗ 2) = 4
Let angle between A and B be θ,

𝑐𝑜𝑠𝜃 =

𝐴∙𝐵
|𝐴| |𝐵|

|𝐴| = √22 + 32 = √13 = 3.6055
|𝐵| = √(−1)2 + 22 = √5 = 2.2361

𝑐𝑜𝑠𝜃 =

𝐴∙𝐵
4
=
= 0.496
|𝐴| |𝐵| 3.6055 ∗ 2.2361
𝜃 = 𝑐𝑜𝑠 −1 0.496 = 60.25°

c) Suppose the position of a particle is given as a function of time by r(t) = x(t)i + y(t)j,
with x(t) = at + b and y(t) = ct2 + d, where a = 1 m/s, b = 1 m, c = 0.225 m/s2, and d
= 1 m. (a) Calculate the average velocity during the time interval from t = 2 s to t =
5 s. (b) Determine the velocity and the speed at t = 3 s.
𝑥(𝑡) = 𝑡 + 1
𝑦(𝑡) = 0.225𝑡 2 + 1
i.

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