Final answer:
To find the minimum speed, use conservation of energy to equate the puck's initial kinetic energy to the potential energy at the top of the ramp. Calculate the height of the ramp using h = L * sin(29 degrees) and solve for speed with the equation v = sqrt(2gh).
Step-by-step explanation:
The question asks to find the minimum speed required for a 130 g puck to reach the top of a frictionless ramp that is 4.1 m long and inclined at 29 degrees. To solve for the minimum speed, we apply the principle of conservation of energy. The initial kinetic energy of the puck must equal the potential energy at the top of the ramp to just reach the top without exceeding it.
In terms of equations, the kinetic energy (KE) is given by KE = (1/2)mv2, and the potential energy (PE) at the top is PE = mgh, where m is the mass of the puck, v is the velocity (or speed), g is the acceleration due to gravity (9.8 m/s2), and h is the height of the ramp. We can find the height h by using the sine of the incline angle times the length of the ramp (h = L * sin(θ)). With no friction, all of the initial kinetic energy will be converted into potential energy at the top of the ramp.
Setting the initial kinetic energy equal to the potential energy at the top gives us:
\((1/2)mv2 = mgh\)
\(v2 = 2gh\)
Now we can solve for v by plug-in the known values (m = 0.13 kg, g = 9.8 m/s2, h = 4.1 * sin(29 degrees)). We can disregard m in this equation because it cancels out on both sides, simplifying our calculation. Finding h and then solving for v will give us the minimum speed required to reach the top of the ramp. The student can calculate these values to find the answer.