Explanation

Explanation

The centripetal force (F) acting on the roller coaster is given by the formula:

F = (m × v^2) / r

Where:

m = net mass of coaster + passengers

v = velocity = 30 m/s

r = radius of the circular track = 30 m

Substituting the values, we get:

F = (m × (30)^2) / 30

= (m × 900) / 30

= 900m / 30

= 900m

So, the centripetal force acting on the roller coaster is 900m.

Explanation

When the velocity increases by 2 times and the radius increases by 4 times, the centripetal force remains the same.

This is because the increase in velocity squared (2^2 = 4) is balanced by the increase in radius (4r), resulting in no net change in the centripetal force.

So, the correct answer is:

F' = F

Explanation

Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t). It can be calculated using the formula:

ω = v / r

Where:

v = linear velocity (in m/s)

r = radius of the circle (in m)

Given:

v = 250 m/s (linear velocity)

r = 100 m (radius of the circle)

ω = v / r

= 250 m/s / 100 m

= 2.5 rad/s

So, the angular velocity of the aircraft is 2.5 rad/sec.

Explanation

The centripetal acceleration of an object moving along a circle of radius 𝑟 with an angular speed 𝜔 is given by the formula 𝑎 = 𝑟 ⋅ 𝜔^2.

This formula indicates that the centripetal acceleration is directly proportional to the radius and the square of the angular speed.

Explanation

Power (P) is defined as the rate at which work is done or energy is transferred. The formula to calculate power is:

P = W / t

Where:

W = work done (in Joules)

t = time (in seconds)

First, we need to calculate the work done (W) by multiplying the force (F) by the displacement (d):

W = F × d

= 2.0 N × 1.0 m ( converted 100 cm to 1.0 m)

= 2.0 J

Now, we can calculate the power output (P) by dividing the work done (W) by the time (t):

P = W / t

= 2.0 J / 4 s

= 0.5 W

So, the power output of the motor is 0.5 W.

Explanation

The formula to calculate work (W) is:

W = F × d

Where:

F = force (in Newtons)

d = displacement (in meters)

Given:

F = 1 N (force)

d = 1 m (displacement)

W = 1 N × 1 m = 1 J

So, the work done is 1 Joule.

Explanation

Work done is equal to Effort x distance.

This is represented mathematically as 

W=F⋅d, where W is work, F is the force (or effort), and d is the distance over which the force is applied.

Explanation

Frictional force is a non-conservative force.

Unlike conservative forces (such as elastic spring force, gravitational force, and electric force), friction dissipates energy as heat and does not store it.

It means the work done by friction depends on the path taken.

Explanation

A farad (F) is the standard unit of capacitance (C) in the International System of Units (SI).

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The SI unit of energy/work is the joule (J)