Force And Acceleration Physics Games : Pipeng Free Online Software

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Pipeng : Physics Translation Motion : Force And Acceleration - Newtons Law Physics Homework BETA Game Module

Force And Acceleration Physics Games

Description : Physics translation motion games : Newtons Law, force and acceleration

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Module List

BETA : Translation : Forces 01 : Newtons Second Law : Force Mass And Acceleration : Beta Physics Homework Game

Description : Newtons Second Law : force = mass times acceleration.

Discussion : According to Newtons second law, the applied force on a free body is proportional to the mass and the acceleration. See Figure Frictionless Mass On A Slope

F = m * a

rearranging

m = F / a

a = F / m

Final velocity

vf = vi + a * t

rearranging

a = (vf - vi) / t

t = (vf - vi) / a

Distance or displacement

d = vi * t + a / 2 * t²

rearranging

a = d / t - a / 2 * t

where

F = force amplitude

m = mass

a = acceleration amplitude

vi = initial velocity amplitude

vf = final velocity amplitude

d = displacement amplitude or distance

t = elapsed time

Angles are in degrees. For convenience, use the degree trig function sind().

BETA : Translation : Forces 02 : Resultant Force Vector : Beta Physics Homework Game

Description : Resultant force vector from the sum of two force vectors.

Discussion : In order to add two force vectors Fa and Fb, they must first be converted into cartesian values which are summed to find the resultant force cartesian values Fx and Fy. Fx and Fy can then be converted back into the resultant vector. See Figure Resultant Force Vector

Fx = Fa * cosd(θa) + Fb * cosd(θb)

Fy = Fa * sind(θa) + Fb * sind(θb)

Fr = √(Fx² + Fy²)

θr = atan2d(Fy, Fx)

To convert from Fr and θr back to Fb and θb

Fx = Fr * cosd(θr)

Fy = Fr * sind(θr)

define custom variables

Fbx = Fx - Fa * cosd(θa)

Fby = Fy - Fa * sind(θa)

Vector Fb

Fb = √(Fbx² + Fby²)

θb = atan2d(Fby, Fbx)

For the special case where θr = 0 and θa and θb are known, find Fb and Fa

Fx = Fr

Fy = 0

define custom variable

aox = -sind(θb) / sind(θa)

Vectors Fb and Fa

Fb = Fr / (aob * cosd(θa) + cosd(θb)

Fa = aob * Fb

where

Fa Fb and Fr = force amplitudes

θa θb θr = force angles

Fx and Fy = cartesian values of resultant force vetor

Fbx Fby = cartesian values of vector Fb

aob = ratio of Fa / Fb

Note : To find Fa and Fb from Fr where θr ≠ 0. Rotate all of the vectors by -θr so that θr = 0;. The angles are in degrees. You are recommended to use the trigonometry degree functions sind(), cosd(), and asind().

BETA : Translation : Forces 03 : Normal And Tangential Force Components For A Force Acting On A surface : Beta Physics Homework Game

Description : Force components for a force acting on a surface.

Discussion : There are two force components acting at right angles, for a force acting on a surface. The normal force component is perpendicular to the surface. The tangential force component is parallel to the surface. See Figure Components Of A Force Acting On A Surface

Fn = F * sind(θ)

Ft = F * cosd(θ)

θ = asind(Fn / F)

θ = atan2d(Fn, Ft)

F = sqrt(Fn² + Ft²)

where

F = applied force

Fn = normal force component

Ft = tangential force component

θ = angle (measured from surface)

The angles are in degrees. You are recommended to use the trigonometry degree functions sind(), cosd(), asind(), acosd() and atan2d().

BETA : Translation : Forces 04 : Friction Force And Resultant Force : Beta Physics Homework Game

Description : Friction force and resultant force.

Discussion : Friction opposes motion. The resultant force equals the thrust force minus the friction force. See Figure Friction Force And Resultant Force

The game has 3 sets of questions with 2 questions per set.

Fr, a

Ff, m

Fr, Ft

The basic equations are :

Fr = Ft - Ff

a = Fr / m

rearranging

Ff = Ft - Fr

Ft = Fr + Ff

Fr = a * m

m = Fr / a

where

Ft = Thrust Force

Ff = Friction Force

Fr = Resultant Force

m = mass

a = acceleration

BETA : Translation : Forces 05 : Tension Force And Weight Force For Hanging Masses : Beta Physics Homework Game

Description : Tension force and weight force for hanging masses.

Discussion : For static equilibrium the forces must balance. See Figure Tension Force And Weight Force For Hanging Masses

The game has 3 sets of questions with 2 questions per set.

T1, T2

T1, F

m1, m2

The basic equations are :

T1 = F + m1 g

T2 = T2 + m2 g

rearranging

T1 = T2 - m2 g

F = T1 - m1 g

m1 = (T1 - F) / g

m2 = (T2 - T1) / g

where

F = Force

T1 = Tension 1

T2 = Tension 2

m1 = mass 1

m2 = mass 2

g = gravity constant = 9.81

BETA : Translation : Forces 06 : Tension Force And Friction Force For Sliding Masses : Beta Physics Homework Game

Description : Tension force and friction force for sliding masses.

Discussion : Two sliding masses are connected together and are being pulled along by a rope connected to mass 1. Both masses have friction forces acting on them. See Figure Tension Force And Friction Force For Sliding Masses

The game has 3 sets of questions with 2 questions per set.

a, T2

F2, T1

m2, F1

The basic equations are :

a = (T1 - F1 - F2) / (m1 + m2)

T2 = F2 + m2 a

rearranging

F2 = T2 - m2 a

T1 = T2 + F1 + m1 a

m2 = (T2 - F2) / a

F1 = T1 - T2 - m1 a

where

F1 = Friction Force

F2 = Friction Force 2

T1 = Tension 1 (Tension force connected to mass 1 pulling the two masses)

T2 = Tension 2 (Tension force between the two masses)

m1 = mass 1

m2 = mass 2

a = acceleration

BETA : Translation : Forces 07 : Force And Moment Equilibrium : Beta Physics Homework Game

Description : Force and moment equilibrium.

Discussion : A point load F is balanced by two reaction forces. For equilibrium the sum of all forces is zero, and the sum of all moments is also zero. Moments have been taken about A, but could also be taken about B. The sum of moments is zero about any point. See Figure Force And Moment Equilibrium

The game has 3 sets of questions with 3 questions per set.

Rb, Ra, b

F, a, b

L, Rb, a

The basic equations are :

Rb = F a / L

Ra = F - Rb

b = L - a

rearranging

F = Ra + Rb

a = Rb L / F

L = F b / Ra = F a / Rb

a = L - b

where

Ra = Reaction Force A

Rb = Reaction Force B

F = Force

L = Length Between Supports

a = Distance From A to F

b = Distance From b to F

BETA : Translation : Forces 08 : Hookes Law : Forces On A Mass And Spring : Beta Physics Homework Game

Description : Hookes law : forces on a mass and spring

Discussion : For a mass and spring stationary at equilibrium the tension force is equal to the gravity force. The spring displacement is proportional to the tensin force divided by the spring constant. See Figure Hookes Law : Forces On A Mass And Spring

The game has 3 sets of questions with 2 questions per set.

T, y

T, m

T, k

The basic equations are :

T = m g

y = T / k

rearranging

m = T / g

T = y k

k = T / y

where

T = Tension Force

m = Mass

g = Gravity Constant = 9.81 m / s²

k = Spring Constant

y = Displacement Of Spring From Equilibrium

BETA : Translation : Slopes 01 : Newtons Second Law : Frictionless Mass On A Slope : Beta Physics Homework Game

Description : Acceleration of a frictionless mass on a slope due to gravity.

Discussion : The acceleration of the mass is due to the component of the gravity force tangential to the slope. See Figure Frictionless Mass On A Slope

a = m * g * sind(θ)

rearranging

θ = asind(a / g)

Gravity Force

Fg = m * g

rearranging

m = Fg / g

Tangential Force

Ft = m * g * sind(θ) = Fg * sind(θ) = m * a

rearranging

m = Ft / a

a = Ft / m

where

m = mass

g = gravity acceleration

a = acceleration of mass

θ = slope angle

Fg = gravity force

Ft = tangential force

Gravity is given here as a constant : g = 9.81 m/s².

BETA : Translation : Slopes 02 : The Point Of Slipping For A Mass On A Slope : Beta Physics Homework Game

Description : The point of slipping for a mass on a slope.

Discussion : At the point of slipping, the brake force is just equal to the tangential component of the gravity force.

Fb = m * g * sind(θ)

rearranging

m = Fb / (g * sind(θ))

θ = asind(Fb / (m * g))

Force components

Fg = m * g

Fn = m * g * cosd(θ)

where

Fb = brake force

Fn = normal force or reaction force

Fg = gravity force

m = mass

g = gravity acceleration

θ = slope angle

Gravity is given here as a constant : g = 9.81 m/s². Angles are in degrees. For convenience, use the degree trig functions cosd(), sind(), asind() and atan2d().

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