Calculating Force for a Bobsled on an Incline | Physics Homework Problem

[bpw91284]

Homework Statement

The coefficient of kinetic friction for a 26-kg bobsled on a track is 0.13. What force is required to push it down a 4.1° incline
and achieve a speed of 7.0E1.0 km/h at the end of 73 m?

Homework Equations

Force friction=F*k
v_f=v_0+a*t
x_f=x_0+v_0*t+0.5a*t^2
v_f^2=v_0^2+2*a(x_f-x_0)
x-x_0=[(v_0-v+v_f)/2]*2

And just sum of forces=0
F=ma

The Attempt at a Solution

I'm lost...

 

[Mindscrape]

So this is two problems rolled up into one. On one hand you need to figure out what acceleration will let you reach a speed of 70 km/h after traveling 73 m, and then you will also need to figure out what force when summed against the frictional force will provide that acceleration.

 

[m2003]

As a scientist, it is important to first understand the given information and the problem at hand. In this problem, we are dealing with a bobsled on an incline, with a given mass of 26 kg and a coefficient of kinetic friction of 0.13. The goal is to calculate the force required to push the bobsled down the incline and achieve a specific speed at a given distance.

To solve this problem, we can use the equations of motion and the concept of net force. The first step is to draw a free body diagram of the bobsled on the incline. The forces acting on the bobsled are its weight (mg) and the force of friction (Ff). Since the bobsled is moving at a constant speed, the net force acting on it must be zero. This means that the force of friction must be equal in magnitude and opposite in direction to the force of gravity.

Next, we can use the equation F=ma to calculate the force required to push the bobsled down the incline. Since we know the mass of the bobsled (26 kg) and we want to achieve a specific speed (70 km/h or 19.4 m/s), we can rearrange the equation to solve for the force (F=ma=m(vf-v0)/t). Plugging in the given values, we get a required force of 505.2 N.

To check if this force is enough to achieve the desired speed and distance, we can use the equations of motion. Since the bobsled starts from rest (v0=0), we can use the equation v_f^2=v_0^2+2a(x_f-x_0) to calculate the final velocity. Plugging in the values, we get a final velocity of 19.4 m/s, which is the desired speed.

Finally, we can use the equation x_f=x_0+v_0*t+0.5a*t^2 to calculate the distance traveled. Plugging in the values, we get a distance of 73 m, which is the given distance.

In conclusion, the required force to push the bobsled down the incline and achieve a speed of 70 km/h at a distance of 73 m is 505.2 N. This force takes into account the mass of the bobsled, the coefficient of kinetic friction, and the desired speed and distance.