A 4.58 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 10.5 N at an angle theta = 25.5° above the horizontal. The coefficient of kinetic friction between the block and the floor is 0.09. What distance does the block travel in a time of 5.90 s after it starts moving?
Fb = m*g = 4.58kg * 9.8N/kg = 44.9 N. =
Force of the block.
Fn = 44.9 - 10.5*sin25.5 = 40.4 N. =
Normal = Force perpendicular to the floor.
Fk = u*Fn = 0.09 * 40.4 = 3.63 N. = Force of kinetic friction.
a = (Fx-Fk)/m = (10.5*cos25.5-3.63)/4.58
= 5.85 m/s^2.
V = a*t = 5.85 * 5.90 = 34.5 m/s.
d = (V^2-Vo^2)/2a = 34.5^2-0)/11.7 = 101.7 m.
The answer was 22.2m...
To find the distance traveled by the block, we need to go step by step:
Step 1: Calculate the net force acting on the block.
The net force is the vector sum of all the forces acting on the block. In this case, we have two forces: the tension force from the cord and the force of friction.
The tension force can be broken down into its horizontal and vertical components: F_h = F * cos(theta) and F_v = F * sin(theta). Given that F = 10.5 N and theta = 25.5°, we can calculate F_h and F_v as follows:
F_h = 10.5 N * cos(25.5°)
F_v = 10.5 N * sin(25.5°)
Step 2: Calculate the force of friction.
The force of friction can be calculated using the formula F_friction = coefficient of friction * Normal force. In this case, the normal force is equal to the weight of the block, which is given by the formula m * g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²). Therefore:
Normal force = m * g = 4.58 kg * 9.8 m/s²
Force of friction = coefficient of friction * Normal force = 0.09 * (4.58 kg * 9.8 m/s²)
Step 3: Calculate the net force.
The net force is the vector sum of the forces. In this case, the horizontal component of tension force and the force of friction act in opposite directions. Therefore, the net force is:
Net force = F_h - Force of friction
Step 4: Calculate the acceleration.
The acceleration of the block can be calculated using Newton's second law, F = m * a. In this case, the net force is acting on the block, so:
Net force = m * a
Rearranging the formula to solve for acceleration:
a = Net force / m
Step 5: Calculate the distance traveled.
The distance traveled can be found using the equation of motion:
d = v_0 * t + (1/2) * a * t²
Since the block starts from rest (v_0 = 0), the equation simplifies to:
d = (1/2) * a * t²
Substituting the values obtained in Step 4, we can calculate the distance traveled by the block.