## SimMechanics Virtual Demos

These demos were designed to complement the lectures and in-class demos of an undergraduate (first year) mechanics class. All demos are .mdl files that were built in the SimMechanics tool box in Matlab 2011. This toolbox allows modeling of rigid body dynamics. Students can vary parameters such as mass, friction, velocity, etc. and visualize the effects on the mechanical system. Instructions for running these files can be found here.

Ramps | Trajectories | Pulleys | Dynamics | Harmonic Motion (ODEs) | Conservation of Momentum

## Ramps:

## Sliding friction

Download the mdl file

In this demo the ramp is lifted at a constant angular velocity (o/sec). The plot of the velocity of the block as a function of time indicates when the block starts to slip.

a. Increase the mass of the block. What happens? Does the angle the board reaches before the block slips (time when v does not = 0) change? Why?

b. Increase the width of the block (changing the contact area). What happens?

c. Increase the coefficient of static friction to 0.5 (keeping dynamic friction the same). What happens? Look at the slope of the dynamic part of the plot. Does it change compared to a. and b.?

d.Now keep the static coefficient of friction the same (0.5) and increase the dynamic friction (0.4). Look at the time it starts to slip and the slope it has when it slips. Explain.

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## Trajectories:

## Ball shot into air with no drag

Download the mdl file

A ball is shot into the air at a specified angle and velocity. Look at the x vs. y plot. (Note: The first time the demo runs, the scale of the view may not be correct. Use the viewing boxes in the simulation window to adjust (or control-D).) Does the shape of the plot make sense?

a. Change the mass of the ball. How does the x vs. y plot change?

b. Double the initial velocity of the ball. By what factor do max height and distance change? Why? (Explain with equations.)

c.Change the angle of the trajectory to 30o and 60o. Look at max x and y. Does this make sense?

## Ball shot into the air with drag

Download the mdl file

A ball is shot into the air at an angle and an initial velocity v0. Air resistance is proportional to the velocity of the ball, Fd = cv. Run the simulation with c = 0 (no drag), v0 = 40 m/s, and mass m = 1. Note: There is an option for Fd = cva. First keep a = 1.

a. Now increase c to 0:2kg/s . What happens to the trajectory? c = 2kg/s?

b.What happens when a = 2, i.e. Fdrag = cv2? Why?

## Beckham takes a goal kick

Download the mdl file

David Beckham takes a free kick from a distance of 20 m from the goal.The ball grazes the head of a 2 m tall opponent standing 10 m from the spot of the kick and goes just under the cross bar of the goal which is 2 m high into the goal. What is the initial velocity at which he kicks the ball? Neglect air resistance. The ball is 20 cm in diameter.

a. Decrease the angle. What happens?

b. Increase the velocity. What happens?

c. Change the mass. What happens?

d. If the ball is kicked at an angle of 30o, is it possible to score?

e.Is the answer unique? (i.e. is there another solution v and that will score a goal?)

## Brick falling on a car

Download the mdl file

A person is charged with breaking the back window of a car by dropping a brick off a bridge 10 m over the motorway. If the car is traveling at 80 km/hr and the back window is sloped at an angle of 45o can the person be guilty as charged?

a. Give the window a very small angle (nearly a sunroof) (angle = 10o). Does the brick hit the window? Try different initial heights and velocities. Does it change what happens? The demo assumes that brick is dropped at just the right time given the height of the bridge and velocity of the car. (Note: Because of the way the graphics work, it does not like an angle of 0o.

b. Give the window a very steep angle, like a pick-up truck (angle = 90o). Does the brick hit? Can you get it to hit by changing the initial height and velocity?

c.What is the critical angle at which the brick will hit the car? Try it.

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## Pulleys:

## Simple pulley

Download the mdl file

In this demo a force is applied to a rope that goes over a pulley and is attached to a weight.

a. Why is acceleration a constant?

b. Keep mass of the pulley = 0 f (we are assuming a massless, frictionless pulley). What happens if you change the force to positive?

c.Determine the force needed so that the block does not move.

## System of pulleys

Download the mdl file

In this demo a weight is attached to a system of three pulleys.

a. Apply a force equal to roughly the weight of the mass. Does it move?

b.What is the force needed to make the block stationary? (Note: it does not like to be completely stationary in how the problem is formulated that requires division by 0.) You can make it very close to 0 to get the idea. Explain.

## Rotating pulley (pulley has mass)

Download the mdl file

A mass is pulled by a rope over a pulley. Start with the mass of the pulley equal to zero.

a. Increase the mass of the pulley. What changes? Why?

b. Make the mass of the pulley equal to the mass of the block. What happens?

c.What if the pulley is ten times heavier than the block?

## Falling block / sliding block connected by pulley

Download the mdl file

A block slides on a frictionless surface and is connected to a hanging block over a pulley.

a. Run it first with a massless pulley.

b. Now increase the mass of the pulley to m = 2kg. Explain the change in the value of acceleration.

c.Make the masses and pulley all the same weight. What happens? Why?

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## Dynamics:

## Falling pen

Download the mdl file

A pen balanced on point starts to fall. It will not slip on the surface unless there is no normal. (Note: the demo shows the motion even after it starts to slip.)

a. Does the angle at which it starts to slip depend on mass, length or radius of the pen?

b. How does the angular acceleration change if you increase the mass, length, radius? Why?

c.Why is the reaction force not a constant value?

## Rolling down a plane

Download the mdl file

A sphere, a solid cylinder, and a hollow cylinder are released from rest at the top of an inclined plane. They all have equal masses and radii. Which one makes it down the ramp first? Why?

a. Change the mass of one of the objects. Does the velocity increase? Why?

b.Change the radius of one of the objects. Does the velocity increase? Why?

## Sliding to rolling transition

Download the mdl file

A ball (mass m, radius r) with an initial velocity (vo) first slides on a plane with friction coefficient (mu). When does it start to roll without sliding? How can you tell this from the plots?

a. Does the mass of the object change when it start to slide without rolling?

b. Change the initial velocity (increase/decrease). How does time it start to roll change?

c. Increase the coefficient of kinetic friction. What happens?

d.If it starts with initial angular velocity and no linear velocity, how does the behavior change?

## Monkey and bananas

Download the mdl file

A monkey climbs up a rope that runs over a pulley and is attached to a big bunch of bananas. As the monkey climbs up the rope, examine the movement of the bananas when:

a. The mass of the monkey is the same as the bananas, the monkey accelerates up the rope at 1m/s^2, and the pulley is massless

b. The mass of the monkey is three times that of the bananas, the monkey accelerates up the rope at 1 m/s^2, and the pulley is massless. Will the monkey reach the bananas? Why?

c. Now make the pulley very heavy. What changes?

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## Harmonic Motion (ODEs):

## Horizontal Spring/Mass/Damper

Download the mdl file

A spring-mass-damper system rests on a frictionless surface. The spring is pulled a distance x0 and released from rest. First examine the system with no damping. Then, increase the damping (keeping the same k and m). What happens to the amplitude? frequency?

a. Change k, what changes?

b.Change m, what changes?

## Vertical Spring/Mass/Damper with Forcing function

Download the mdl file

This simulation is a vertical spring with a forcing function. Run the simulation without drag and with no forcing function. What is different about the vertical spring and a horizontal spring (in terms of the graphs)?

a. Add drag.

b. Make the system underdamped, overdamped, and critically damped.

c. Add a forcing function. What changes?

d. Make the system close to resonance. What happens? Note: At resonance it will not solve. Very high forcing frequency?

## Simple Pendulum

Download the mdl file

A pendulum is an oscillating system. Use r = 1;m = 1; initial angle of displacement = 30oo, and L = 9. The plot shows angular velocity vs. t and angle vs. angular velocity. Why is the latter plot an circle? (Note: it looks like an ellipse because the axes are not equal spacing.

a. What changes if you change m? L?

b. What happens if you change 0?

c.Make 0 = 179o. What happens? Note: do not use > 180o.

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## Conservation of Momentum:

## Elastic collision of two bodies in 1D on a frictionless track

Download the mdl file

Two gliders collide perfectly elastically on a frictionless track. Make the two masses equal and the initial velocity of the red block

vred = 0. Compare the velocities of the two blocks.

a. Now makevred = -3m/sso it is a ’head on collision’. Does the final velocity of the red block change compared to when it was stationary? Explain.

b.Now makemyellow = 2mredand give the initial velocityvred = 0. Does the yellow one move after the collision? Why?

## Inelastic collision of two bodies in 1D on a frictionless track

Download the mdl file

Now the collision is perfectly inelastic (the blocks stick together).

Look at the change in velocities of the two blocks.

Explain.

## Elastic collision of two bodies on 2D on a frictionless plane

Download the mdl file

This shows the effects of elastic collisions on a 2D frictionless plane. Give the blocks equal masses and initial velocities. Look at the velocities after the collision. Explain.

a. Now make myellow = 2mred, but still with equal initial velocities. Explain.

b.Now assign vyellow = 2vred. Which block has greater velocity after collision?

Why?

## Inelastic collision of two bodies on 2D on a frictionless plane

Download the mdl file

This is similar to the previous example but with inelastic collisions. Give the blocks equal masses and initial velocities. Look at the velocities after the collision. Explain.

a. Now makemyellow = 2mred, but still with equal initial velocities. Explain.

b. Now give the blocks equal masses, butvyellow = 2vred. Do the blocks travel in the same direction as in (a.)?

Explain.

## Newtons Pendulum

Download the mdl file

This shows a classic Newton’s pendulum with 5 balls. Displace 1 ball of mass m = 1 by an angle = 30 degrees. Look at the plot of alpha, omega, and theta. What does a negative omega mean? How can you calculate the velocity in the horizontal direction of the ball at contact?

a. Double the mass of the balls. What changes? Why?

b. Displace 2 balls. What happens? Why?

c. Displace 4 balls. What happens? Why?

d.Decrease the initial angle. What happens? Why?

## Newton’s Pendulum with unequal masses

Download the mdl file

This is a modified Newton’s pendulum with 3 balls. Two of the balls are stuck together (effectively m = 2m, which mimics a two ball system with balls of different masses.

Run the demo.

Why do both masses keep moving after impact (in contrast to the demo above where all balls are equal masses?

Which one has greater velocity?

Why?

## Two bodies connected by spring on 1D on a frictionless track

Download the mdl file

Two gliders rest on a frictionless track connected by a spring. The spring is given an initial displacement. The green dot indicates the centre of mass. Determine the motion of the centre of mass when:

a. The blocks have equal mass and zero initial velocity.

b. The blocks have different masses and zero initial velocity.

c.The blocks have different masses and an initial velocity.

## Man with bike wheel on rotating stool

Download the mdl file

This is the classic demo for angular momentum. A person sits on a stool that can rotate and holds a rotating bike wheel with the axis of rotation horizontal between the two hands. The person rotates the bike wheel so that the axis of rotation is vertical.

What happens?

a. Change the mass of the man.

b. Change the mass of the wheel.

## Ice skater brings arms in

Download the mdl file

An ice skater brings her arms from outstretched to down.

What happens to her angular velocity?

Momentum?

Explain.

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