A contestant in a winter games event pushes a 41.0 kg block of ice in the positive direction across a frozen lake as shown in the Figure (a). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03.
Incomplete.
To determine the force required to push the block of ice, we need to consider the forces acting on the block.
1. Normal force (N): This is the force exerted by the surface on the block perpendicular to the surface. In this case, it is equal to the weight of the block, which can be calculated as the mass of the block multiplied by the acceleration due to gravity (9.8 m/s^2). So, N = 41.0 kg * 9.8 m/s^2.
2. Force of gravity (mg): This is the force due to the block's weight and acts in a vertically downward direction. It can be calculated as the mass of the block multiplied by the acceleration due to gravity (9.8 m/s^2). So, mg = 41.0 kg * 9.8 m/s^2.
3. Static friction force (fs): This is the force that opposes the motion of the block when it is at rest. The maximum value of static friction force can be calculated by multiplying the coefficient of static friction (0.1) with the normal force (N). So, fs = 0.1 * N.
4. Kinetic friction force (fk): This is the force that opposes the motion of the block when it is in motion. The value of kinetic friction force can be calculated by multiplying the coefficient of kinetic friction (0.03) with the normal force (N). So, fk = 0.03 * N.
In this case, since the block is being pushed in the positive direction, the static friction force must be overcome first before the block starts moving. Once the block is in motion, the kinetic friction force needs to be overcome to maintain the block's motion.
To determine the force required to push the block, we need to compare the maximum static friction force with the applied force. If the applied force is greater than the maximum static friction force, the block will start moving. If the block is already in motion, the applied force needs to overcome the kinetic friction force to maintain its motion.
You have not mentioned the applied force in this question. If you provide the value of the applied force, I can further help you calculate the forces involved.
To find the force needed to push the block of ice, we need to consider both the static friction and the kinetic friction.
First, let's determine the maximum static friction force. The maximum static friction force can be calculated using the formula:
\( f_{\text{max}} = \mu_s \cdot N \),
where \( f_{\text{max}} \) is the maximum static friction force, \( \mu_s \) is the coefficient of static friction, and \( N \) is the normal force.
The normal force can be determined by multiplying the mass of the block of ice by the acceleration due to gravity, which is \( N = m \cdot g \), where \( m \) is the mass of the block of ice (41.0 kg) and \( g \) is the acceleration due to gravity (approximately 9.8 m/s²).
So, the maximum static friction force is:
\( f_{\text{max}} = 0.1 \cdot (41.0 \, \text{kg} \cdot 9.8 \, \text{m/s}^2) \).
To find the actual force required to overcome static friction, we need to compare it to the force applied by the contestant. If the force applied by the contestant is greater than the maximum static friction force, the block of ice will start moving.
Once the block of ice is in motion, the force of friction changes to kinetic friction. The force of kinetic friction can be calculated using the formula:
\( f_{\text{kinetic}} = \mu_k \cdot N \),
where \( f_{\text{kinetic}} \) is the force of kinetic friction and \( \mu_k \) is the coefficient of kinetic friction.
To summarize:
1. Calculate the maximum static friction force using \( f_{\text{max}} = \mu_s \cdot N \).
2. Compare the force applied by the contestant to the maximum static friction force. If the applied force is greater than the maximum static friction force, the block of ice will start moving.
3. Once the block of ice is in motion, use the kinetic friction force formula \( f_{\text{kinetic}} = \mu_k \cdot N \) to find the force of kinetic friction.