5. 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. (3 marks)
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?
start:
0.18 m g = 0.18 * 24 * 9.81 Newtons
constant speed:
0.10 m g = 0.10 * 24 * 9.81 Newtons
To find the force required to start the toboggan moving, you need to calculate the maximum force of static friction. Once the toboggan starts moving, the force required to keep it moving at a constant speed is equal to the force of kinetic friction.
a) To find the force required to start the toboggan moving, you need to calculate the maximum force of static friction. The formula for static friction is given by:
F_static = μ_static * N
where F_static is the force of static friction, μ_static is the coefficient of static friction, and N is the normal force.
To calculate the normal force, you can use the equation:
N = m * g
where m is the mass of the toboggan and papers (24 kg in this case), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Therefore, N = 24 kg * 9.8 m/s^2 = 235.2 N
Now, you can calculate the maximum force of static friction:
F_static = 0.18 * 235.2 N = 42.3 N
Therefore, Salim must pull with a force of 42.3 N to get the toboggan to start moving.
b) Once the toboggan is in motion, you need to calculate the force of kinetic friction. The formula for kinetic friction is given by:
F_kinetic = μ_kinetic * N
where F_kinetic is the force of kinetic friction, μ_kinetic is the coefficient of kinetic friction, and N is the normal force (same as before).
Using the same value for N, you can calculate the force of kinetic friction:
F_kinetic = 0.10 * 235.2 N = 23.5 N
Therefore, to keep the toboggan moving at a constant speed, Salim needs to pull with a force of 23.5 N.