Answer:
The algebraic equation is:

Explanation:
Given information:
mb = book's mass
vb = tangential speed
R = radius of the path
Question: Derive an algebraic equation for the vertical force, Fv = ?
To derive the equation, we need to draw a force diagram for this case, please, see the attached diagram. As you can see, there are three types of forces acting on the system. Two up and one of the weight acting down. Therefore, the algebraic equation is as follows:

The variables were defined above and g is the gravity.
Answer:
Juan and Kuri complete one revolution in the same time, but Juan travels a shorter distance and has a lower speed.
Explanation:
Since Juan is closer to the center and Kuri is away from the center so we can say that Juan will move smaller distance in one complete revolution
As we know that the distance moved in one revolution is given as

also the time period of revolution for both will remain same as they move with the time period of carousel
Now we can say that the speed is given as

so Juan will have less tangential speed. so correct answer will be
Juan and Kuri complete one revolution in the same time, but Juan travels a shorter distance and has a lower speed.
Answer:
V₂ = 1.5 m/s
Explanation:
given,
speed of the first piece = 6 m/s
speed of the third piece = 3 m/s
speed of the second fragment = ?
mass ratios = 1 : 4 : 2
fragment break fly off = 120°
α = β = γ = 120°
sin α = sin β = sin γ = 0.866
using lammi's theorem

A,B and C is momentum of the fragments

4 x V₂ = 2 x 3
V₂ = 1.5 m/s
The question is incomplete. Here is the entire question.
A jetboat is drifting with a speed of 5.0m/s when the driver turns on the motor. The motor runs for 6.0s causing a constant leftward acceleration of magnitude 4.0m/s². What is the displacement of the boat over the 6.0 seconds time interval?
Answer: Δx = - 42m
Explanation: The jetboat is moving with an acceleration during the time interval, so it is a <u>linear</u> <u>motion</u> <u>with</u> <u>constant</u> <u>acceleration</u>.
For this "type" of motion, displacement (Δx) can be determined by:

is the initial velocity
a is acceleration and can be positive or negative, according to the referential.
For Referential, let's assume rightward is positive.
Calculating displacement:


= - 42
Displacement of the boat for t=6.0s interval is
= - 42m, i.e., 42 m to the left.
Answer:
d. 37 °C
Explanation:
= mass of lump of metal = 250 g
= specific heat of lump of metal = 0.25 cal/g°C
= Initial temperature of lump of metal = 70 °C
= mass of water = 75 g
= specific heat of water = 1 cal/g°C
= Initial temperature of water = 20 °C
= mass of calorimeter = 500 g
= specific heat of calorimeter = 0.10 cal/g°C
= Initial temperature of calorimeter = 20 °C
= Final equilibrium temperature
Using conservation of heat
Heat lost by lump of metal = heat gained by water + heat gained by calorimeter
