Solving Mechanics Question: Motorcycle + Rider Masses & Reactions

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In summary, the motorcycle has a mass of 250kg and a rider with a mass of 80kg. The center of mass of the motorcycle is located at a vertical line midway between the wheels, and when the rider is on the motorcycle, his center of mass is 1m behind the front wheel. The motorcycle has a total of 1449 Newtons of cw torque when the rider is not on the motorcycle and 1785 N when the rider is on the motorcycle.
  • #1
jimmy p
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Im doing Mechanics module 2 at college (the only one!) and while working through an exercise i got stumped by this question.


"A motorcycle has a mass of 250kg, and it's rider whose mass is 80kg. The centre of mass of the motorcycle lies on a vertical line midway between its wheels. When the rider is on the motorcycle, his centre of mass is 1m behind the front wheel. Find the vertical reaction forces acting through the front and rear wheels when:

(i) the rider is not on the motorcycle.
(ii) the rider is on the motorcycle."

Then it has a stupid picture of a man on a motobike with the distance 1.4m between the centres of the two wheels (so the centre of mass is as 0.7m)

Now i looked in the back of the book after many failed attempts and the answers are:

(i) 1225N for front wheel, 1225N for rear wheel
(ii) 1449N for front wheel, 1785N for real wheel.

i can't get those answers!


EDIT take gravity as 9.8 instead of 10.
 
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  • #2
I am assuming you are doing rotational equilibrium, is that right?

So balance the torques: choose the rear (draw it on the left) wheel as the point of rotation. Your clockwise torques are from the bike that is acting at its c-o-m, and the guy on the bike. The only ccw torque is from the front wheel. What force at the front wheel will produce a torque equal to the sum of the other torques?

ps: I get a total cw torque of 2028.6 Nm for the second part.
 
Last edited:
  • #3
Well, you certainly ought to be able to get

"(i) 1225N for front wheel, 1225N for rear wheel"!

With the man not on the motorcycle, the weight of the motorcycle, 250kg* 9.8= 2450 Newtons is evenly divided between front and rear wheel: 2450/2= 1225 Newtons.

The man himself has weight 80kg*9.8= 784 Newtons. He is 1 meter from the front wheel so, choosing the front wheel as "center of rotation", his that would be a torque of 784 N-m counter clockwise. That must be offset by the same torque from the force on the rear wheel: its distance from the front wheel is 1.4 m so, taking F as the force on the rear wheel, 1.4F= 784 or F= 784/1.4= 560 N. Of course, the front wheel supports the rest of his weight: 784- 560= 224 Newtons.

Adding in the 1225 Newtons on each wheel due to the motorcycle itself, The front wheel is uspporting 1225+224= 1449 Newtons and the rear wheel 1225+ 560= 1785 N as advertised!
 
  • #4
*slaps forehead* Man I am a dumbass, i kept converting mass into Newtons so i was getting 24500! what a loser...

Cheers HallsOfIvy, and thanks for your answer to Chi Meson, maybe i should explain better in future!
 

1. What is the formula for calculating the total mass of a motorcycle and rider?

The formula for calculating the total mass of a motorcycle and rider is M = mm + mr, where M is the total mass, mm is the mass of the motorcycle, and mr is the mass of the rider.

2. How do you calculate the reaction forces on the motorcycle and rider?

The reaction forces on the motorcycle and rider can be calculated using Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. This means that the reaction force on the motorcycle is equal in magnitude and opposite in direction to the force exerted by the rider and vice versa.

3. What is the significance of calculating the forces on the motorcycle and rider?

Calculating the forces on the motorcycle and rider is important for understanding the dynamics of the system and ensuring that the vehicle is stable and safe to operate. It also allows for the optimization of the vehicle's performance and handling.

4. How does the mass of the rider affect the overall performance of the motorcycle?

The mass of the rider affects the overall performance of the motorcycle in several ways. A heavier rider will increase the total mass of the system, which can impact acceleration and braking. The rider's weight distribution can also affect the balance and handling of the motorcycle.

5. What are some common sources of error when solving mechanics questions involving motorcycle and rider masses and reactions?

Some common sources of error when solving mechanics questions involving motorcycle and rider masses and reactions include neglecting to consider all the forces acting on the system, using incorrect or incomplete data, and making calculation errors. It is important to carefully analyze the problem and double-check all calculations to minimize these errors.

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