Find the acceleration down the ramp:
skateboarder starts from rest at the top of a 12.5 m slick ramp that makes a 25 degree angle with the horizontal. (coefficient of rolling friction is negligible). Combined mass of skateboarder and skateboard = 75 kg.
Net force down= mass*a
mg*SinTheta=m*a solve for a.
If you had friction, it would be like this:
mg*sinTheta-mu*mg*CosTheta=ma
To find the acceleration down the ramp, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, we can consider the net force acting on the skateboarder and skateboard system.
First, we need to find the component of the weight that acts down the ramp. The weight can be separated into two components: the force parallel to the ramp (mg*sinθ) and the force perpendicular to the ramp (mg*cosθ).
Given:
- Length of the ramp, L = 12.5 m
- Angle of the ramp with the horizontal, θ = 25°
- Combined mass of skateboarder and skateboard, m = 75 kg
- Acceleration down the ramp, a = ?
Step 1: Calculate the force parallel to the ramp
The force parallel to the ramp is given by:
F_parallel = mg*sinθ
Step 2: Calculate the net force down the ramp
The net force down the ramp is equal to F_parallel because there are no other significant forces acting horizontally:
Net force = F_parallel = mg*sinθ
Step 3: Apply Newton's second law of motion
Using Newton's second law of motion, we have:
Net force = mass * acceleration
Substituting the known values:
mg*sinθ = ma
Step 4: Solve for acceleration
Divide both sides of the equation by the mass (m):
g*sinθ = a
Substitute the values of g (acceleration due to gravity, approximately 9.8 m/s^2) and the angle θ into the equation:
a = 9.8 m/s^2 * sin(25°)
Now, we can calculate the acceleration down the ramp:
a ≈ 4.15 m/s^2
Therefore, the acceleration down the ramp is approximately 4.15 m/s^2.