How to do this
In a bowling game, a player rolls a small ball along the ground. The diagram shows the action the player as he starts to swing his arm forward at $A$, to the point when the bail is rolling along the ground at C .
The player exerts a forward force on the ball between $\mathbf{A}$ and $B$.
(a) (i) State how the motion of the ball at $\mathbf{C}$ differs from that at B .
(2)
$\qquad$ $\qquad$ $\qquad$ $\qquad$
(ii) The player applies a forward force for 0.20 s and the ball leaves the player's hand at a speed of $3.0 \mathrm{~m} \mathrm{~s}^{-1}$.

Calculate the average forward force that the player applies to the ball.
mass of ball, $m_{1}=1.5 \mathrm{~kg}$ $\qquad$ $\qquad$ $\qquad$
Average forward force $=$ $\qquad$
(b) The ball rolls along the ground until it collides with a stationary ball of mass 1.2 kg . After the collision both balls roll off at an angle to the original direction of the moving ball as shown in the diagrams.

Question

How to do this
In a bowling game, a player rolls a small ball along the ground. The diagram shows the action the player as he starts to swing his arm forward at $A$, to the point when the bail is rolling along the ground at C .
The player exerts a forward force on the ball between $\mathbf{A}$ and $B$.
(a) (i) State how the motion of the ball at $\mathbf{C}$ differs from that at B .
(2)
$\qquad$ $\qquad$ $\qquad$ $\qquad$
(ii) The player applies a forward force for 0.20 s and the ball leaves the player's hand at a speed of $3.0 \mathrm{~m} \mathrm{~s}^{-1}$.

Calculate the average forward force that the player applies to the ball.
mass of ball, $m_{1}=1.5 \mathrm{~kg}$ $\qquad$ $\qquad$ $\qquad$
Average forward force $=$ $\qquad$
(b) The ball rolls along the ground until it collides with a stationary ball of mass 1.2 kg . After the collision both balls roll off at an angle to the original direction of the moving ball as shown in the diagrams.

Accepted Answer

∻Solution∻ ‖ a ⋮ At position B, the ball is still being acted upon by the player's forward force, which means it is accelerating. At position C, the ball has left the player's hand and is rolling along the ground, experiencing no further forward force, thus it moves at a constant velocity. ‖ ‖ b ⋮ To calculate the average forward force applied by the player, we can use Newton's second law: $$F = ma$$. First, we need to find the acceleration of the ball. The ball leaves the player's hand at a speed of $3.0 \, \mathrm{m/s}$ after $0.20 \, \mathrm{s}$. The acceleration can be calculated as: $$a = \frac{\Delta v}{\Delta t} = \frac{3.0 \, \mathrm{m/s} - 0}{0.20 \, \mathrm{s}} = 15 \, \mathrm{m/s^2}$$. Now, using the mass of the ball, we can find the force: $$F = m \cdot a = 1.5 \, \mathrm{kg} \cdot 15 \, \mathrm{m/s^2} = 22.5 \, \mathrm{N}$$. ‖ ∻Answer∻ ⚹ 22.5 N ⚹ ∻Key Concept∻ ⚹ Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Equation: $$F = ma$$ (Net force equals mass times acceleration) ⚹ ∻Explanation∻ ⚹ The average forward force can be calculated using the mass of the ball and the acceleration derived from the change in velocity over time. This demonstrates the relationship between force, mass, and acceleration. ⚹

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