Question
Two ice skaters collided while moving toward each other on the ice. The first skater had a mass of 42 kg and was moving to the right before the collision. The second skater was moving to the left before the collision. The force of the second skater caused the first skater to accelerate to the left at a rate of 1.5 m/s2 . What force did the first skater exert on the second skater?(1 point) Responses 35 N 35 cap n 28 N 28 cap n 45 N 45 cap n 63 N
Answers
GPT-4o mini
To determine the force that the first skater exerted on the second skater, we can use Newton's second law of motion, which states that \( F = m \cdot a \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
In this case, we need to first calculate the force exerted by the second skater on the first skater, which resulted in the first skater accelerating to the left at \( 1.5 \, \text{m/s}^2 \).
The mass of the first skater \( m_1 \) is \( 42 \, \text{kg} \), and the acceleration \( a_1 \) is \( 1.5 \, \text{m/s}^2 \) to the left (which we will take as negative since it's the opposite direction of their initial movement to the right).
Calculating the force:
\[
F = m_1 \cdot a_1 = 42 \, \text{kg} \cdot (-1.5 \, \text{m/s}^2) = -63 \, \text{N}
\]
The negative sign indicates that the force is directed to the left. According to Newton's third law, the first skater exerts an equal and opposite force on the second skater:
\[
F_{\text{first on second}} = -F_{\text{second on first}} = 63 \, \text{N}
\]
Therefore, the downward force that the first skater exerted on the second skater is **63 N**. The correct response is:
**63 N**
In this case, we need to first calculate the force exerted by the second skater on the first skater, which resulted in the first skater accelerating to the left at \( 1.5 \, \text{m/s}^2 \).
The mass of the first skater \( m_1 \) is \( 42 \, \text{kg} \), and the acceleration \( a_1 \) is \( 1.5 \, \text{m/s}^2 \) to the left (which we will take as negative since it's the opposite direction of their initial movement to the right).
Calculating the force:
\[
F = m_1 \cdot a_1 = 42 \, \text{kg} \cdot (-1.5 \, \text{m/s}^2) = -63 \, \text{N}
\]
The negative sign indicates that the force is directed to the left. According to Newton's third law, the first skater exerts an equal and opposite force on the second skater:
\[
F_{\text{first on second}} = -F_{\text{second on first}} = 63 \, \text{N}
\]
Therefore, the downward force that the first skater exerted on the second skater is **63 N**. The correct response is:
**63 N**