A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping.
Which one makes it furthest up the ramp?

a) Block
b) Ball
c) Both reach the same height.

Respuesta :

Answer:

b) Ball

Explanation:

The block is sliding and ball is rolling . Ball have greater energy as it has both linear kinetic energy and rotational kinetic energy . So it will have additional rotational energy as the linear kinetic energy of both of them will be equal because linear velocity of both are equal.

As ball has greater total kinetic energy , height attained by it will be greater on the ramp

The ball and block will reach the same height because they have the same potential energy.

The given parameters;

  • let the mass of the block and ball, = m
  • let the velocity of the block and ball, = v

The kinetic energy of each object is calculated and follows;

K.E = ¹/₂mv²

The potential energy of each object is calculated as follows;

P.E = mgh

Based on the principle conservation of mechanical energy;

P.E = K.E

Since both objects have the same mass and velocity, their kinetic energy will be the same and the maximum kinetic energy is equal to the maximum potential energy. Applying the principle conservation of mechanical energy, both object will reach the same height.

Thus, we can conclude that the ball and block will reach the same height because they have the same potential energy.

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