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Shot put is a track-and-field event in which athletes propel a metal shot, or ball, by pushing it away from their shoulder. In junior events, shots of different sizes are used for different categories of competitors.

The shot masses and forces applied for four competitors are shown. Which shot will have the greatest acceleration?

(1 point)
Responses

5 kg and 40 N
5 kg and 40 N

5 kg and 30 N
5 kg and 30 N

4 kg and 40 N
4 kg and 40 N

6 kg and 30 N

1 answer

To find out which shot will have the greatest acceleration, we can use Newton's second law of motion, which states that \( F = ma \), or rearranged as \( a = \frac{F}{m} \), where \( F \) is the force applied, \( m \) is the mass of the shot, and \( a \) is the acceleration.

Let's calculate the acceleration for each competitor:

  1. 5 kg and 40 N: \[ a = \frac{F}{m} = \frac{40 \text{ N}}{5 \text{ kg}} = 8 \text{ m/s}^2 \]

  2. 5 kg and 30 N: \[ a = \frac{F}{m} = \frac{30 \text{ N}}{5 \text{ kg}} = 6 \text{ m/s}^2 \]

  3. 4 kg and 40 N: \[ a = \frac{F}{m} = \frac{40 \text{ N}}{4 \text{ kg}} = 10 \text{ m/s}^2 \]

  4. 6 kg and 30 N: \[ a = \frac{F}{m} = \frac{30 \text{ N}}{6 \text{ kg}} = 5 \text{ m/s}^2 \]

Now, let's compare the accelerations:

  • 5 kg with 40 N: \( 8 \text{ m/s}^2 \)
  • 5 kg with 30 N: \( 6 \text{ m/s}^2 \)
  • 4 kg with 40 N: \( 10 \text{ m/s}^2 \)
  • 6 kg with 30 N: \( 5 \text{ m/s}^2 \)

The shot put with the greatest acceleration is the 4 kg shot with 40 N, which has an acceleration of \( 10 \text{ m/s}^2 \).