A sled loaded with bricks has a total mass of 17.0 kg and is pulled at constant speed by a rope inclined at 20.0o above the horizontal. The sled moves a distance of 17.0 m on a horizontal surface. The coefficient of kinetic friction between the sled and surface is 0.420 . (a) What is the tension in the rope?
M*g = 17 * 9.8 = 166.6 N. = Wt. of the total mass.
Fn = 166.6*Cos 0 - T*sin20 = 166.6-0.342T = Normal force.
Fk = u*Fn = 0.420*(166.6-0.342T) = 70-0.144T Newton.
T*Cos20-Fk = M*a.
0.940T-(70-0.144T) = 17*0
0.94T-70+0.144T = 0
1.084T = 70
T = 64.6 N. = Tension in the rope.
To find the tension in the rope, we need to consider the forces acting on the sled. There are three main forces to consider:
1. The gravitational force (mg) acting vertically downwards, where m is the mass of the sled and g is the acceleration due to gravity (9.8 m/s^2).
2. The normal force (N) acting vertically upwards from the surface. This force is equal in magnitude but opposite in direction to the gravitational force.
3. The force of kinetic friction (fk) acting horizontally in the opposite direction of motion.
Since the sled is moving at a constant speed, the net force acting on it must be zero. Therefore:
Sum of horizontal forces = fk
Sum of vertical forces = mg - N = 0
Let's solve for each of these forces step by step:
1. Force of kinetic friction (fk):
The force of kinetic friction can be calculated using the equation:
fk = μk * N
where μk is the coefficient of kinetic friction and N is the normal force.
2. Normal force (N):
The normal force is equal in magnitude but opposite in direction to the gravitational force, and can be calculated using:
N = mg
where m is the mass of the sled and g is the acceleration due to gravity.
3. Tension in the rope:
To find the tension in the rope, we need to analyze the forces in the vertical direction. Since the sled is pulled at a constant speed, the tension force in the rope must balance the gravitational force. Therefore:
T - mg = 0
where T is the tension in the rope.
Now we can solve for the tension in the rope by following these steps:
Step 1: Calculate the force of kinetic friction (fk) using the given coefficient of kinetic friction (μk) and the normal force (N).
fk = μk * N
Step 2: Calculate the normal force (N) using the mass of the sled (m) and the acceleration due to gravity (g).
N = mg
Step 3: Set up an equation to find the tension in the rope (T).
T - mg = 0
Step 4: Solve the equation for T to find the tension in the rope.
Note: Make sure to convert the angle from degrees to radians if necessary for any trigonometric calculations.