Questions: A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 95.0 kg, and he is accelerating at 1.17 m / s^2 backward. (a) What is the force of friction (in N) between the losing player's feet and the grass? (Enter the magnitude.) N (b) What force (in N) does the winning player exert on the ground to move forward if his mass plus equipment is 112 kg? (Enter the magnitude.) N

A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 95.0 kg, and he is accelerating at 1.17 m / s^2 backward.
(a) What is the force of friction (in N) between the losing player's feet and the grass? (Enter the magnitude.)
N
(b) What force (in N) does the winning player exert on the ground to move forward if his mass plus equipment is 112 kg? (Enter the magnitude.)
N

Transcript text: A brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 N on him. The mass of the losing player plus equipment is 95.0 kg , and he is accelerating at $1.17 \mathrm{~m} / \mathrm{s}^{2}$ backward. (a) What is the force of friction (in $N$ ) between the losing player's feet and the grass? (Enter the magnitude.) $\square$ N (b) What force (in N ) does the winning player exert on the ground to move forward if his mass plus equipment is 112 kg ? (Enter the magnitude.) $\square$ N

Solution

Solution Steps

Step 1: Determine the Net Force on the Losing Player

The net force $ F_{\text{net}} $ on the losing player can be calculated using Newton's second law: \[ F_{\text{net}} = m \cdot a \] where $ m = 95.0 \, \text{kg} $ and $ a = 1.17 \, \text{m/s}^2 $.

\[ F_{\text{net}} = 95.0 \, \text{kg} \times 1.17 \, \text{m/s}^2 = 111.15 \, \text{N} \]

Step 2: Calculate the Force of Friction

The force of friction $ F_{\text{friction}} $ can be found by subtracting the net force from the applied force: \[ F_{\text{friction}} = F_{\text{applied}} - F_{\text{net}} \] where $ F_{\text{applied}} = 800 \, \text{N} $.

\[ F_{\text{friction}} = 800 \, \text{N} - 111.15 \, \text{N} = 688.85 \, \text{N} \]

Step 3: Determine the Force Exerted by the Winning Player on the Ground

The force exerted by the winning player on the ground can be calculated using Newton's third law. The force the winning player exerts on the ground is equal in magnitude and opposite in direction to the force the ground exerts on the winning player. This force can be calculated using the same principle as in Step 1: \[ F_{\text{net, winning}} = m_{\text{winning}} \cdot a \] where $ m_{\text{winning}} = 112 \, \text{kg} $ and $ a = 1.17 \, \text{m/s}^2 $.

\[ F_{\text{net, winning}} = 112 \, \text{kg} \times 1.17 \, \text{m/s}^2 = 131.04 \, \text{N} \]

Since the winning player must exert a force to counteract the friction and move forward, the total force exerted on the ground is: \[ F_{\text{ground}} = F_{\text{net, winning}} + F_{\text{friction}} \]

However, since the friction force is not given for the winning player, we assume the force exerted by the winning player is equal to the net force calculated: \[ F_{\text{ground}} = 131.04 \, \text{N} \]