The coefficient of kinetic friction for a 34.3 kg bobsleigh on a track is 0.150. What external force is required to push it down a 5.60° incline and achieve a speed of 60.12 km/h at the end of 75.2m ?
PE=KE + W(fr)
mgh =mv²/2 + F(fr)•s
m•g•s•sinα =mv²/2 +μ•m•g•cosα•s
Solve for μ
To calculate the external force required to push the bobsleigh down the incline, we need to consider the forces acting on the bobsleigh. The main forces involved are the gravitational force and the frictional force.
1. Gravitational force:
The gravitational force acting on the bobsleigh is equal to its weight, which is given by the formula: F_gravity = m * g, where m is the mass of the bobsleigh and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = 34.3 kg * 9.8 m/s^2
2. Frictional force:
The frictional force can be calculated using the formula: F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force acting on the bobsleigh.
The normal force is the component of the gravitational force that acts perpendicular to the incline. It can be calculated using the formula: F_normal = m * g * cos(θ), where θ is the angle of the incline (5.60°).
F_normal = 34.3 kg * 9.8 m/s^2 * cos(5.60°)
Now, we can calculate the frictional force:
F_friction = 0.150 * F_normal
Finally, to achieve the desired speed of 60.12 km/h (or 16.7 m/s) at the end of a distance of 75.2 m, we need to apply a net force along the incline to overcome the combined effect of the gravitational force and the frictional force.
Net force = F_gravity + F_friction
Remember to convert the angle from degrees to radians before performing the calculations.
I hope this explanation helps you understand how to calculate the external force required in this scenario.