Final answer:
To find the minimum speed a 140 g puck needs to make it to the top of a frictionless ramp, we can use the principle of conservation of energy. By equating the kinetic energy at the bottom of the ramp to the gravitational potential energy at the top, we can solve for the minimum speed. Plugging in the given values, we find the minimum speed to be approximately 10.7 m/s.
Step-by-step explanation:
To calculate the minimum speed shoes a 140 g puck needs to make it to the top of a frictionless ramp, we can use the principle of conservation of energy. At the top of the ramp, all of the puck's initial kinetic energy will be converted into gravitational potential energy. The equation we can use is:
KE + PE = PE
Where KE is the kinetic energy, PE is the potential energy, and PE is the potential energy at the top of the ramp. The kinetic energy is given by:
KE = 0.5 * m * v^2
Where m is the mass of the puck and v is its speed. The potential energy at the top of the ramp is given by:
PE = m * g * h
Where g is the acceleration due to gravity and h is the height of the ramp. Substituting the values into the equations and solving for v, we get:
v = sqrt(2 * g * h)
Plugging in the values of g = 9.8 m/s^2 and h = 5.5 m, we find:
v = sqrt(2 * 9.8 * 5.5) = 10.7 m/s
Therefore, the minimum speed the puck needs is approximately 10.7 m/s.