A 3.26 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 10.4 N at an angle theta = 29.0° above the horizontal. The coefficient of kinetic friction between the block and the floor is 0.10. What is the speed of the block 3.1 s after it starts moving?
To find the speed of the block 3.1 seconds after it starts moving, we can break down the problem into several steps:
Step 1: Find the net force acting on the block.
The net force can be found by considering the horizontal forces acting on the block. The force pulling the block, F = 10.4 N, can be resolved into horizontal and vertical components. The horizontal component, Fx, is given by Fx = F * cos(theta), where theta is the angle above the horizontal. Substituting the values, we get Fx = 10.4 N * cos(29.0°).
The force of kinetic friction, Fk, can be found by multiplying the coefficient of kinetic friction, μk = 0.10, by the normal force acting on the block. The normal force, N, is equal to the weight of the block, N = m * g, where m is the mass of the block and g is the acceleration due to gravity. Substituting the values, we get N = 3.26 kg * 9.8 m/s^2.
The force of kinetic friction can now be calculated as Fk = μk * N.
The net force, Fnet, is the difference between the force pulling the block and the force of kinetic friction. Fnet = Fx - Fk.
Step 2: Determine the acceleration of the block.
The acceleration, a, can be calculated using Newton's second law, Fnet = m * a, where Fnet is the net force and m is the mass of the block. Rearranging the equation, we get a = Fnet / m.
Step 3: Calculate the final velocity of the block.
Using the equation for uniformly accelerated motion, v = u + a * t, where v is the final velocity, u is the initial velocity (which is zero in this case as the block starts from rest), a is the acceleration, and t is the time, we can substitute the values to find the final velocity.
Now, let's calculate the speed of the block 3.1 seconds after it starts moving.
Step 1: Find the net force acting on the block.
Angle theta = 29.0°
Force F = 10.4 N
Mass of the block m = 3.26 kg
Acceleration due to gravity g = 9.8 m/s^2
Coefficient of kinetic friction μk = 0.10
Fx = F * cos(theta) = 10.4 N * cos(29.0°)
N = m * g = 3.26 kg * 9.8 m/s^2
Fk = μk * N
Fnet = Fx - Fk
Step 2: Determine the acceleration of the block.
a = Fnet / m
Step 3: Calculate the final velocity of the block.
v = u + a * t
Substituting the values and solving these equations will give us the speed of the block 3.1 seconds after it starts moving.