A 5.56 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 10.7 N at an angle theta = 17.0° above the horizontal, as shown in the Figure. The coefficient of kinetic friction between the block and the floor is 0.06. What is the speed of the block 6.1 s after it starts moving?
Wb = m*g = 5.56kg * 9.8N/kg = 54.5 N. =
Wt. of block
Fb = 54.5N @ 0o. = Force of the block.
Fp = 54.5*sin(0) = 0. Force parallel to
floor.
Fv = 54.5*cos(0) - 10.7*sin17 =51.4 N. =
Force perpendicular to floor.
Fk = u*Fv = 0.06 * 51.4 = 3.08 N.=Force
of kinetic friction.
Fap-Fp-Fk = ma.
10.7*cos17-0-3.08 = 5.56*a
10.5-3.08 = 5.56a
7.43 = 5.56a
a = 1.34 m/s^2.
V = Vo + at = 0 + 1.34*6.1 = 8.16 m/s.
To find the speed of the block 6.1 seconds after it starts moving, we can follow these steps:
1. Resolve the force F into its vertical and horizontal components. The horizontal component of the force is F_horizontal = F * cos(theta), and the vertical component of the force is F_vertical = F * sin(theta).
F_horizontal = 10.7 N * cos(17°) = 10.7 N * 0.953 = 10.20 N
F_vertical = 10.7 N * sin(17°) = 10.7 N * 0.292 = 3.12 N
2. Calculate the normal force acting on the block. The normal force is equal to the weight of the block since it's on a horizontal surface. The weight is given by the formula: weight = mass * gravity
Weight = mass * gravity = 5.56 kg * 9.8 m/s^2 = 54.49 N
3. Calculate the frictional force acting on the block. The frictional force is given by the formula: friction_force = friction_coefficient * normal_force
Here, the friction coefficient is given as 0.06 and the normal force is the weight of the block.
Friction_force = friction_coefficient * normal_force = 0.06 * 54.49 N = 3.27 N
4. Calculate the net force on the block in the horizontal direction. The net force is the difference between the horizontal component of the applied force and the frictional force.
Net_force = F_horizontal - Friction_force = 10.20 N - 3.27 N = 6.93 N
5. Calculate the acceleration of the block using Newton's second law: net_force = mass * acceleration.
Acceleration = Net_force / mass = 6.93 N / 5.56 kg = 1.246 m/s^2
6. Calculate the final velocity of the block using the equation of motion: final_velocity = initial_velocity + acceleration * time.
The initial velocity is zero because the block starts from rest.
Final_velocity = acceleration * time = 1.246 m/s^2 * 6.1 s = 7.61 m/s
Therefore, the speed of the block 6.1 seconds after it starts moving is 7.61 m/s.