Dynamics Solved Problems

Projectile Motion

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2.1 - An object is dropped from a height of 10m, determine how long it falls for and its impact velocity. Ignore air resistance.

Dynamics Projectile Motion Solved Problem

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2.2 - An object is thrown straight up from the ledge. What is the maximum height that the object reaches? How long until the object hits the ground? What is the impact velocity?

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2.3 - A soccer ball is kicked at an angle. What is the maximum height that it achieves and how far away does it hit the ground?

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2.4 - A soccer ball is kicked at an empty net. Will the player score?

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2.5 - A soccer ball is kicked off a ledge. Where does it land?

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Circular Motion

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3.1 - A belt driven wheel with a radius of 30 cm is spinning at 300 rpm. What is the angular velocity of the wheel, and how fast is the belt moving?

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3.2 - A wind turbine with 30m blades spins at 22 rpm. Find the angular velocity of the turbine and the tangential velocity of the blade tip.

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3.3 - A spinning wheel with a 5 cm radius accelerates constantly from 2,000 rpm to 6,000 rpm over 4 seconds. Find the angular acceleration of the wheel, as well as the tangential acceleration of an outermost point on the wheel.

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3.4 - A performer is spinning fire at a show at 2 revolutions per second. The chain is 1 m long and the fireball at the end weighs 150 g. What is the tension in the chain? (hint: it equals the centripetal force). Ignore gravity for this one, as it's spinning horizontally.

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3.5 - A bicycle constantly accelerates from rest to 5m/s during 10 seconds. What is the angular acceleration of the wheels about their axles, and how many revolutions will the wheels go through during this period.

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3.6 - A vehicle drives around a flat circular corner with a radius of 100m. If the maximum coefficient of static friction between the wheels and pavement is 0.85, then what is the maximum speed that the car can maintain without skidding?

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3.7 - Find the velocity and acceleration of point Q after 5 seconds if the meshed gears initially start from a rest.

Dynamics rigid body rotation meshed gear example

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3.8 - Wheel A is driving wheel B with a belt. If the system starts at a rest, determine the velocity and acceleration of point P after 6 seconds.

Dynamics rigid body rotation belt drive example

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Kinetics

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4.1 - Determine what the force F must be for the box to accelerate at 2m/s^2

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4.2 - Determine the acceleration of the box

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4.3 - Determine the acceleration of the box

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4.4 - Determine the kinetic coefficient of friction

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4.5 - Determine the direction and magnitude of the acceleration for this box on a slope

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4.6 - Determine the direction and magnitude of the acceleration for this box on a slope

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4.7 - The 25kg mass is being raised by a cable with an upward acceleration of 2m/s^2, determine the tension in the cable

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4.8 - The 25kg mass is being lowered by a cable with a downward acceleration of 2m/s^2, determine the tension in the cable

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4.9 - Determine the tension in the cable if the 25kg mass is not accelerating

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4.10 - Determine the cable tension and the acceleration of the masses in this Atwood Machine

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4.11 - Determine the tension in the cable and acceleration of the masses in this system

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Work and Energy

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5.1 - A force pushes the block 10m along a level surface. How much work does the force do over this distance?

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5.2 - An oblique force pushes the block 10m along a level surface. How much work does the force do over this distance?

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5.3 - A force lifts a block by 5m. How much work is done by the applied force? How much work is done by the block’s weight?

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5.4 - A 1.2kg block is sliding across a surface with an initial velocity of 30cm/s. Determine the average friction force if it comes to a complete stop in 1.5m.

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5.5 - A rollercoaster car descends a slope and then completes a loop the loop. Determine its speed at the top of the points B and C. Assume no friction for this one.

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5.6 - The pendulum is released from a rest at point A. Determine the speed of the ball at points B and C. Assume no friction at the pin.

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5.7 - This iconic hippy van can accelerate to 100km/h from a rest in a whopping 37s. Find the average power exerted by the motor. Keep it simple and ignore friction.

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5.8 - A 7hp motor lifts a load at 0.5m/s. What mass can it lift at this speed?

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5.9 - A crane lifts a van by 5m in 10 seconds. What is the average power exerted by the crane motor? Assume the crane is lifting at a constant speed.

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Impulse and Momentum

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6.1 - Determine the average force that the bat exerts on the baseball during the impulse.

Dynamics Solved Impulse & Momentum Problem

Solution

6.2 - Like most physics example problems, some unfortunate person has found themself in a highly improbable scenario. In this case, the person is wearing ice skates, standing on ice, and is about to catch a bowling ball flying to wards them at 6m/s. What will be the velocity be of the person holding the ball, after it is caught? Assume no friction because of the skates/ice situation. RIP person.

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6.3 - A golf club exerts an average force of 3kN on a golf ball for 0.001s. Determine the magnitude of the impulse and also the velocity of the golf ball immediately after impact.

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6.4 - The van is about to crash head-on into a wall at 50km/h. If the impact lasts 0.03s, then calculate the average force acting on the van during the crash.

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6.5 - Two objects collide head-on. Determine the velocity of each object after impact if the collision is perfectly elastic.

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6.6 - Two objects collide head-on. Determine the velocity of each object after impace if the collision is perfectly inelastic.

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6.7 - Two objects collide head-on. Determine the velocity of each object after impact if the collision's coefficient of restitution is 0.75.

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6.8 - Two objects have an oblique collision in the x-y plane. Determine the velocity of each object after impact if the collision is perfectly elastic.

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6.9 - Two objects have an oblique collision in the x-y plane. Determine the velocity of each object after impact if the collision is perfectly plastic.

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6.10 - Two objects have an oblique collision in the x-y plane. Determine the velocity of each object after impact if the collision's coefficient of restitution is 0.8.

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Rigid Body Rotation

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7.1 - Member AB is connected to the stationary frame with sliders. Determine the velocity of A using relative motion (vector) analysis.

Dynamics Relative Motion Vector Analysis Solved Problem Sliders

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7.2 - Member AB is connected to the stationary frame with sliders. Determine the velocity of A using relative motion (scalar) analysis.

Dynamics Relative Motion Scalar Analysis Solved Problem Sliders

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7.3 - Member AB is connected to the stationary frame with sliders. Determine the velocity of A using the instantaneous centre of zero velocity method.

Dynamics Instantaneous Centre of Zero Velocity Solved Problem Sliders

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7.4 - Member AB is connected to the stationary frame with sliders. Determine the velocity of A using absolute motion analysis.

Dynamics rigid body rotation absolute motion analysis double slider example

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7.5 - Member AB is rotating at a constant angular velocity of 8 rad/s. Determine the velocity of point C on the sliding collar at this instant using relative motion (vector) analysis.

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7.6 - Member AB is rotating at a constant angular velocity of 8 rad/s. Determine the velocity of point C on the sliding collar at this instant using relative motion (scalar) analysis.

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7.7 - Member AB is rotating at a constant angular velocity of 8 rad/s. Determine the velocity of point C on the sliding collar at this instant using the instantaneous centre of zero velocity method.

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7.8 - Member AB is rotating at a constant angular velocity of 8 rad/s. Determine the velocity of point C on the sliding collar at this instant using absolute motion analysis.

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