Work and Energy Test. 3

Since there is no displacement of the wall, the work done on the wall is zero, according to the physics definition of work (W=Fd).

Escape velocity v_e = √(2GM/R). Since 'v' is inversely proportional to the square root of 'R', halving 'R' to R/2 will multiply the velocity by √2.

Work is defined as force multiplied by displacement (W=Fd). If the displacement is zero, the work done is zero, regardless of the magnitude of the force.

Given ½m₁v₁² = ½m₂v₂², we can rearrange to get v₁²/v₂² = m₂/m₁. Taking the square root gives v₁/v₂ = √(m₂/m₁).

Einstein's famous equation, E=mc², states that energy (E) and mass (m) are equivalent and can be converted into one another, with c² being the conversion factor.

Since F = ma, the centripetal force is F_c = ma_c. Substituting a_c = v²/r gives F_c = mv²/r.

For any gravitationally bound system, like a satellite in orbit, the total mechanical energy (KE + PE) is negative. A positive or zero total energy would mean the object is not in a bound orbit and can escape.

Stretching or compressing an elastic object, like a rubber band or a spring, stores energy in it in the form of elastic potential energy.

Centripetal force is the net force that produces centripetal acceleration. It is not a fundamental force but the net result of other forces (like tension, gravity, or friction).

Centripetal acceleration (a_c) is the acceleration that causes an object to change its direction to follow a circular path, and it is always directed towards the center of the circle.

The tangential linear velocity of a point on a rotating object is given by the product of its distance from the axis (radius) and its angular velocity.

As the body falls, its potential energy is converted into kinetic energy. In the absence of air resistance, the total mechanical energy (PE + KE) remains constant.

The force (friction) is opposed to the motion, so the angle is 180°. W = Fd cos(180°) = 200 N * 10 m * (-1) = -2000 J.

Moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion, just as mass is a measure of resistance to changes in linear motion.

To find the work done by a variable force, we calculate the area under the Force-Displacement graph by dividing it into a large number of small rectangular intervals and summing their areas.

Centripetal acceleration can be expressed as a_c = v²/r or, by substituting v=rω, as a_c = rω².

While degrees are commonly used, the standard SI unit for angular displacement, which is necessary for rotational motion equations, is the radian.

Using the right-hand rule, if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular velocity vector.

Angular velocity (ω) is defined as the rate at which the angular displacement (θ) changes with respect to time (ω = Δθ/Δt).

A full circle (360°) corresponds to an arc length equal to its circumference (2πr). Since θ = s/r, one revolution is θ = (2πr)/r = 2π radians.