Work Done on Motorbike: Calculating Force & Distance

[victoration1]

Homework Statement

A girl uses a 3.0 m long ramp to push her 110 kg motorbike up to a trailer, the floor of which
is 1.2 m above the ground. How much work is done on the motorbike?

Homework Equations

W=FD where W is work, F is force and D is distance travelled.

The Attempt at a Solution

Assuming that 3.0m long ramp means a base length of 3.0 meters, then the hypotenuse of the ramp must be approximately 3.2meters. Thus, the bike must travel 3.2 meters in a diagonal direction. What I cannot find is the force which will push this bike up the ramp.

 

[amy andrews]

Think of the free body diagram for this. Apart the force the girl exerts on the bike (and I'm assuming there's no friction, since it isn't included in the problem) what are the forces acting on the bicycle?

 

[victoration1]

Gravity. Which on an inclined plane like this, can be divided into two components; perpendicular and parallel. Calculating the degree of the ramp I find 22 degrees by arctan1.2/3.0. Using cos22 x 1078 I find the perpendicular component of gravity,1000N, which is the same as the normal force exerted by the ramp on the bike. The parallel force is 404N when I use sin22 x 1078, and it is the amount of downward (relative to ramp) force acting on the bike if nothing supports it.
The problem is, given these components, I still cannot find work because the applied force of the girl isn't given.

Thanks for your reply.

 

[amy andrews]

Exactly. The weight of the bike, the normal force, and the force the girl exerts. These forces are equal, if the girl pushes the bike up with constant velocity.
Take a look at the attached free body diagram, write a couple of equations (with the x and y components), and the force the girl exerts should be pretty clear.
Let me know if you have any questions :)

 

[rwisz]

Since the bike is moving at a constant velocity, the net force must be zero. However, there are two forces acting on the bike: the force of gravity and the force applied by the girl. To calculate the force applied by the girl, we can use Newton's second law which states that force is equal to mass times acceleration (F=ma). Since the bike is moving at a constant velocity, the acceleration is zero and thus the force applied by the girl must be equal to the force of gravity (Fg=mg). Plugging in the values, we get F=(110 kg)(9.8 m/s^2)= 1078 N.

Now, we can calculate the work done on the motorbike using the equation W=FD. Since we have already calculated the force (F=1078 N) and the distance travelled (D=3.2 m), we can simply plug in these values to get the work done on the motorbike. Therefore, the work done on the motorbike is approximately 3449 Joules (W=1078 N x 3.2 m = 3449 J).

In conclusion, the work done on the motorbike is approximately 3449 Joules. It is important to note that this calculation assumes ideal conditions and does not take into account any external factors such as friction or air resistance.