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Dynamics Solved Problems

​projectile motion | circular motion | kinetics | work & energy | impulse & momentum | rigid body rotation


Projectile Motion

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
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
Solution

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?
Dynamics Projectile Motion Solved Problem
Solution

​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?
Dynamics Projectile Motion Solved Problem
Solution

​2.4 - A soccer ball is kicked at an empty net. Will the player score?
Dynamics Projectile Motion Solved Problem
Solution

​2.5 - A soccer ball is kicked off a ledge. Where does it land?
Dynamics Projectile Motion Solved Problem
Solution


Circular Motion

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
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?
Dynamics Solved Circular Motion Problem
Solution

​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.
Dynamics Solved Circular Motion Problem
Solution

​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.
Dynamics Solved Circular Motion Problem
Solution

​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. ​
Dynamics Solved Circular Motion Problem
Solution

​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.
Dynamics Solved Circular Motion Problem
Solution

​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?
Dynamics Solved Circular Motion Problem
Solution

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
Solution

​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
Solution


Kinetics

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
4.1 - Determine what the force F must be for the box to accelerate at 2m/s^2
Dynamics Solved Kinetics Problem
Solution

​4.2 - Determine the acceleration of the box
Dynamics Solved Kinetics Problem
Solution

​4.3 - Determine the acceleration of the box
Dynamics Solved Kinetics Problem
Solution

​4.4 - Determine the kinetic coefficient of friction
Dynamics Solved Kinetics Problem
Solution

​4.5 - Determine the direction and magnitude of the acceleration for this box on a slope
Dynamics Solved Kinetics Problem
Solution

​4.6 - Determine the direction and magnitude of the acceleration for this box on a slope
Dynamics Solved Kinetics Problem
Solution

​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
Dynamics Solved Kinetics Problem
Solution

​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
Dynamics Solved Kinetics Problem
Solution

​4.9 - Determine the tension in the cable if the 25kg mass is not accelerating
Dynamics Solved Kinetics Problem
Solution

​4.10 - Determine the cable tension and the acceleration of the masses in this Atwood Machine
Dynamics Solved Kinetics Problem
Solution

​4.11 - Determine the tension in the cable and acceleration of the masses in this system
Dynamics Solved Kinetics Problem
Solution


​Work and Energy

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
5.1 - A force pushes the block 10m along a level surface. How much work does the force do over this distance?
Dynamics Solved Work & Energy Problem
SOLUTION

​5.2 - An oblique force pushes the block 10m along a level surface. How much work does the force do over this distance?
Dynamics Solved Work & Energy Problem
SOLUTION

​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?
Dynamics Solved Work & Energy Problem
SOLUTION

​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.
Dynamics Solved Work & Energy Problem
SOLUTION

​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.
Dynamics Solved Work & Energy Problem
SOLUTION

​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.
Dynamics Solved Work & Energy Problem
SOLUTION

​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.
Dynamics Solved Work & Energy Problem
SOLUTION

​5.8 - ​A 7hp motor lifts a load at 0.5m/s. What mass can it lift at this speed?
Dynamics Solved Work & Energy Problem
SOLUTION

​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.
Dynamics Solved Work & Energy Problem
SOLUTION


Impulse and Momentum

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
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.
Dynamics Solved Impulse & Momentum Problem
solution

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.
Dynamics Solved Impulse & Momentum Problem
solution

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.
Dynamics Solved Impulse & Momentum Problem
solution

​6.5 - Two objects collide head-on. Determine the velocity of each object after impact if the collision is perfectly elastic.
Dynamics Solved Impulse & Momentum Problem
solution

​6.6 - Two objects collide head-on. Determine the velocity of each object after impace if the collision is perfectly inelastic.
Dynamics Solved Impulse & Momentum Problem
solution

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.
Dynamics Solved Impulse & Momentum Problem
solution

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.
Dynamics Solved Impulse & Momentum Problem
solution

​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.
Dynamics Solved Impulse & Momentum Problem
solution

​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.
Dynamics Solved Impulse & Momentum Problem
solution


Rigid Body Rotation

The solutions to these practice problems are visible to much my appreciated Patreon supporters. By choosing the $10 tier on Patreon you can immediately unlock all solutions. ​
 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
Solution

​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
Solution

​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
Solution

​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
Solution

​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.
Dynamics rigid body rotation relative vector analysis solution
Solution

​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.
Dynamics rigid body rotation relative scalar analysis solution
Solution

​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.
Dynamics rigid body rotation centre of instantaneous velocity solution
Solution

​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.
Dynamics rigid body rotation absolute motion analysis solution
Solution
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