In loading a fish delivery truck, a person pushes a block of ice up a 200 incline at constant speed. The push is 150N in magnitude and parallel to the incline. The block has a mass of 35.0 kg. What is the force of kinetic friction on the block of ice?
150N because it moves at constant speed. Forces are hence at equilibrium, there is no net force, so the friction force parallel to the slope is equal to the force pushed with.
To find the force of kinetic friction on the block of ice, we need to use the equation for friction. The force of kinetic friction can be calculated using the equation:
\(f_{\text{friction}} = \mu_k \cdot N\)
Where:
\(f_{\text{friction}}\) is the force of kinetic friction.
\(\mu_k\) is the coefficient of kinetic friction.
\(N\) is the normal force.
First, let's determine the normal force acting on the block of ice. The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the block of ice acts straight down, perpendicular to the incline. We can find the normal force using the equation:
\(N = mg\cdot \cos(\theta)\)
Where:
\(m\) is the mass of the block (35.0 kg).
\(g\) is the acceleration due to gravity (-9.8 m/s²).
\(\theta\) is the angle of the incline (200°).
Substituting the given values, we have:
\(N = (35.0 \text{ kg}) \cdot (-9.8 \text{ m/s²})\cdot \cos(200°)\)
Now, let's calculate the normal force.
\(N = (35.0 \text{ kg}) \cdot (-9.8 \text{ m/s²})\cdot \cos(200^\circ)\)
The normal force depends on the angle of the incline, so we need to calculate the value of \(\cos(200^\circ)\). Note that the cosine of 200° is the same as the cosine of (180° + 20°), which is equivalent to the cosine of 20°. Therefore, we can rewrite the equation as:
\(N = (35.0 \text{ kg}) \cdot (-9.8 \text{ m/s²})\cdot \cos(20^\circ)\)
Now, calculate the value of \(\cos(20^\circ)\) and substitute it into the equation:
\(N = (35.0 \text{ kg}) \cdot (-9.8 \text{ m/s²}) \cdot \cos(20^\circ)\)
After finding the value of \(N\), we can finally calculate the force of kinetic friction using the equation:
\(f_{\text{friction}} = \mu_k \cdot N\)
However, the coefficient of kinetic friction is not given in the problem. Without this value, we cannot find the exact force of kinetic friction. The coefficient of kinetic friction is a material-specific property and must be provided to obtain an accurate answer.