Question

4.0 kg
a 4.0 kg bat swings to the left and
makes contact with a 0.5 kg ball,
exerting +78 n of force.
0.5 kg
which object accelerates
more quickly after impact?
+78 n -78 n
the ball accelerations are
equal.
the bat not enough
information.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law is \( F = ma \), which can be rearranged to \( a=\frac{F}{m} \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration.

Step2: Determine Forces on Bat and Ball

By Newton's third law, the force exerted by the bat on the ball (\( F_{\text{ball}} = +78\,\text{N} \)) and the force exerted by the ball on the bat (\( F_{\text{bat}}=- 78\,\text{N} \)) have the same magnitude (\( |F| = 78\,\text{N} \)).

Step3: Calculate Acceleration of the Ball

For the ball, \( m_{\text{ball}} = 0.5\,\text{kg} \) and \( F = 78\,\text{N} \). Using \( a=\frac{F}{m} \), we get \( a_{\text{ball}}=\frac{78}{0.5}=156\,\text{m/s}^2 \).

Step4: Calculate Acceleration of the Bat

For the bat, \( m_{\text{bat}} = 4.0\,\text{kg} \) and \( F = 78\,\text{N} \). Using \( a=\frac{F}{m} \), we get \( a_{\text{bat}}=\frac{78}{4.0} = 19.5\,\text{m/s}^2 \).

Step5: Compare Accelerations

Since \( 156\,\text{m/s}^2>19.5\,\text{m/s}^2 \), the ball has a greater acceleration.

Answer:

The ball