Salim has a paper route. In the winter time, he puts his newspapers on a toboggan to pull them through the snow. The combined mass of the papers and the toboggan is 24 kg. The coefficient of static friction between the toboggan and the snow is 0.18. The coefficient of kinetic friction between the toboggan and the snow is 0.10.
a. With how much force must Salim pull in order to get the toboggan to start moving?
b. How much force is needed to keep the toboggan moving at a constant speed? Please can I get a step by step solution and answer
To solve these questions, we will use the concepts of friction and Newton's laws of motion.
a. To find the force required to get the toboggan to start moving, we need to consider the static friction. The formula for static friction is:
\[ F_{\text{static}} = \mu_{\text{static}} \cdot N \]
where \( \mu_{\text{static}} \) is the coefficient of static friction and \( N \) is the normal force. In this case, the normal force is equal to the weight of the toboggan and the papers, which can be calculated by multiplying the mass by the acceleration due to gravity \( g \):
\[ N = (m_{\text{papers}} + m_{\text{toboggan}}) \cdot g \]
\[ N = (24 \, \text{kg}) \cdot (9.8 \, \text{m/s}^2) \]
\[ N = 235.2 \, \text{N} \]
Now, substituting the values into the formula:
\[ F_{\text{static}} = (0.18) (235.2 \, \text{N}) \]
\[ F_{\text{static}} = 42.28 \, \text{N} \]
Therefore, Salim must pull with a force of approximately 42.28 N to get the toboggan to start moving.
b. To find the force needed to keep the toboggan moving at a constant speed, we need to consider the kinetic friction. The formula for kinetic friction is:
\[ F_{\text{kinetic}} = \mu_{\text{kinetic}} \cdot N \]
where \( \mu_{\text{kinetic}} \) is the coefficient of kinetic friction. Using the same normal force value we found in part a, we can substitute the values into the formula:
\[ F_{\text{kinetic}} = (0.10) (235.2 \, \text{N}) \]
\[ F_{\text{kinetic}} = 23.52 \, \text{N} \]
Therefore, a force of approximately 23.52 N is needed to keep the toboggan moving at a constant speed.