A father gives his son a ride by pulling a sled across the rough snow. The father runs across the snow with a constant acceleration while pulling the sled at F = 75.0 N, at 30 deg. above the horizontal. The combined mass the sled and son is 30.0 kg. The coefficient of kinetic friction between the sled and the snow is Uk = 0.200.
a) What is the magnitude of the normal force exerted on the sled-son system?
sum of Fx: -fk + 75cos30 = max
sum of Fy: n-mg +75sin30 = may
This is as far as I got and I'm not even sure if it's correct. Please provide a concise solution so that I can see exactly what's going on. I need to master Newton's laws. I have pressure of college approaching. If I see the way, I can solve problems. Also, I don't just want solution as not knowing what is happening won't help me on a test. I have tried to solve it on paper. It is tedious to put my inaccurate solution on here. Thank you so much.
b) What is the magnitude of the acceleration of the sled-son system?
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a) To find the magnitude of the normal force exerted on the sled-son system, we first need to determine the net force acting on the system in the x-direction and y-direction.
Let's analyze the forces in the x-direction:
- We have the force F, which the father exerts on the sled, given as F = 75.0 N at an angle of 30 degrees above the horizontal.
- The force of kinetic friction, fk, opposes the motion of the sled and acts in the opposite direction to F.
Using Newton's second law (sum of F = ma) in the x-direction, we have:
-fk + 75cos30 = max
In the y-direction, the forces are:
- The normal force, n, exerted by the snow on the sled-son system.
- The weight of the sled-son system, mg, where m is the total mass and g is the acceleration due to gravity.
- The vertical component of the force F, which is 75sin30.
Applying Newton's second law in the y-direction:
n - mg + 75sin30 = may
Now, we can solve these two equations simultaneously to find the magnitude of the normal force exerted on the sled-son system.
b) To determine the magnitude of the acceleration of the sled-son system, we can use the result obtained in part a.
Once we have the value of the normal force, n, we can substitute it into the equation obtained in the x-direction (-fk + 75cos30 = max) to solve for the acceleration, a.
We also know the value of the coefficient of kinetic friction, Uk (given as 0.200), which can be used to calculate the force of kinetic friction, fk = Uk * n.
Substituting these values into the equation, we can find the magnitude of the acceleration of the sled-son system.