Question

You and some friends visit the Florida State Fair and decide to play a game. To play the game you must slide a metal hockey-type puck up a wooden ramp so that it drops through a hole at the top of the ramp. Your prize, if you win, is a large, stuffed gorilla. You realize the secret to winning is giving the puck just enough velocity at the bottom of the ramp to make it to the hole. You estimate the distance from the bottom of the ramp to the hole at about 3 m, and the ramp appears to be inclined with an angle of 10o from the horizontal. You just got out of physics class and recall the coefficient of static friction between steel and wood is 0.1 and the coefficient of kinetic friction between steel and wood is 0.08. The mass of the puck is about 1 kg. You decide to impress your friends by sliding the puck at the precise speed on the first try so as to land it in the hole. You slide the puck at 2.0 m/sec. Do you win the stuffed poodle? Let g = 10 m/s2. Note: A slightly too hard throw will win since your aim is so good the puck would drop in the hole.

Answer 1

No you didn't win the stuffed poodle

Step-by-step explanation:

From the question we are told that

The distance of the ramp to the hole is d = 3 m \

The angle of inclination is
`\theta  =  10^o`

The coefficient of static friction is
`\mu_s = 0.1`

The coefficient of kinetic friction is
`\mu_k = 0.08`

The mass of the puck is m = 1 kg

The velocity of the first slide is
`v_1  =  2.0 m/s`

Generally the kinetic energy at the bottom of the ramp is equal the energy loss due to friction and this can be mathematically represented as

`(1)/(2) m *  v^  2 =  \mu_k * [m *  g] *  cos (theta )  *  d`

=>
`(1)/(2)  *  v^  2 = 0.08 * 9.8 *  cos (10 )  *  3`

=>
`v=  2.17 \  m/s`

Comparing the relative velocity obtained and the velocity of your first throw we can see that you didn't win the stuffed animal