Calculating Acceleration On A Ramp

[cameronpalte]

A student is skateboarding down a ramp that is inclined 20 degrees with respect to the horizontal. The speed of the skateboarder at the top of the ramp is 3.0 m/s and the speed of the skateboarder at the bottom of the ramp is 7.6 m/s. The frictional force between the ramp and the skateboard is 67 N.

(a) If the combined weight of the student and the skateboard is 654 N, determine the acceleration of the student/skateboard system.

I've tried f=ma saying that
(654)-(67) = 654/9.8 [a]

Would that work?

 

[SHISHKABOB]

don't forget to take into account the fact that the student is moving parallel to the surface of the ramp, while his weight is directed straight down. This means that only the component of his weight that is parallel to the surface of the ramp is going to affect his acceleration in that direction.

 

[cameronpalte]

Which component of his weight would be parallel? I would assume that the 654 N of the combined weight would be?

 

[SHISHKABOB]

"weight" is the force that a person (or object) feels due to gravity. Since gravity is always directed straight down, the force, and thus the weight, is directed straight down.

 

[Nickie]

Your approach is correct. The equation F=ma can be used to calculate the acceleration of the skateboarder. In this case, the total force acting on the skateboarder is the net force, which is the difference between the weight (654 N) and the frictional force (67 N). This net force is equal to the mass (m) of the skateboarder multiplied by the acceleration (a).

So, the equation becomes:

654 N - 67 N = (m)(a)

Solving for a, we get:

a = (654 N - 67 N) / m = (587 N) / m

Now, we need to find the mass of the skateboarder. We can use the formula for weight (W=mg) and solve for m:

m = W/g = 654 N / 9.8 m/s^2 = 66.7 kg

Substituting this value back into the equation for acceleration, we get:

a = (587 N) / (66.7 kg) = 8.8 m/s^2

Therefore, the acceleration of the student/skateboard system is 8.8 m/s^2. This means that the skateboarder is speeding up at a rate of 8.8 m/s^2 as they move down the ramp.