A pool cue ball is hit by a stick with a force of 12.5N. The ball's mass is 0.17kg. Distance between cue ball and blue ball= 1.2m. Distance between blue ball and hole = 0.7m. There is friction between both balls and table- coefficient of 0.005. Will the blue ball reach the hole?
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and see whether enough work is done by the cue stick.
To determine if the blue ball will reach the hole, we need to calculate the net force acting on the blue ball and compare it to the force it needs to overcome the friction and move towards the hole.
1. Find the force applied by the pool cue ball on the blue ball:
- The force applied by the stick is 12.5N, but this force is transferred to the blue ball when they collide.
- This force can be calculated using Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration.
- Rearranging the formula to solve for acceleration, we get a = F/m.
- Plugging in the values for force (12.5N) and mass (0.17kg), we have a = 12.5N / 0.17kg.
2. Calculate the acceleration of the blue ball:
- The acceleration represents how fast the blue ball will move when struck by the pool cue ball.
- The acceleration can be calculated by dividing the force by the mass.
- Using the values from step 1, calculate the acceleration of the blue ball.
3. Determine the force of friction:
- The force of friction between the blue ball and the table can be calculated using the formula Ff = μ * N.
- The normal force (N) is the weight of the blue ball, which can be calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s^2).
- Multiply the normal force by the coefficient of friction (0.005) to find the force of friction.
4. Calculate the net force:
- To find the net force, subtract the force of friction from the force exerted on the blue ball.
- The net force will indicate whether the blue ball can overcome the force of friction and move towards the hole.
- Subtract the force of friction from the force applied to the blue ball.
5. Determine if the blue ball will reach the hole:
- If the net force is greater than zero, then the blue ball will move towards the hole.
- If the net force is equal to zero, then the blue ball will not move and will not reach the hole.
- If the net force is negative, then the force of friction is greater than the force applied, preventing the blue ball from reaching the hole.
By following these steps and plugging in the given values, you can determine whether the blue ball will reach the hole.