A 10-KG block is pulled along a rough horizontal floor by a 12-N force acting at a 30 degrees angle with respect to the horizontal. The block accelerates at 0.1 m/s2. Calculate
A....... the weight of the block
B...... the force of friction acting on the block
C.... the normal force acting in the block
d.........the coefficient of kinetic friction uk
e..... the force of static friction acting on the block if the pulling force must be 20 N acting at 30 degrees in other start the block moving along the floor
F.... the coefficient of static friction Us
Can you do any of these yourself?
Have you ever seen the expression
Weight = M g ?
Do you know how to calculate friction forces and the relationship to friction coefficients?
In part "e", is "in other start" supposed to be "in order to start"?
i can but can u work so i can compare mine
I would rather advise students who show some sign of thought and effort, and who do not just post or paste assigned questions and expect worked-out answers.
To solve this problem, we will use Newton's second law of motion and the equations of friction. Let's break it down step by step:
A. The weight of the block can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the block is 10 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 10 kg × 9.8 m/s^2
Weight = 98 N
Therefore, the weight of the block is 98 N.
B. The force of friction acting on the block can be calculated using the formula:
Force of friction = coefficient of friction × normal force
Since the block is on a rough horizontal floor, there is friction opposing its motion. The force of friction is equal to the product of the coefficient of kinetic friction (uk) and the normal force acting on the block. To find the force of friction, we first need to calculate the normal force.
C. The normal force can be calculated using the formula:
Normal force = weight of the block × cosine(angle of the inclined force)
In this case, the angle is 0 degrees with respect to the horizontal direction, so the cosine of 0 degrees is 1. Therefore, the normal force is equal to the weight which is 98 N.
Normal force = 98 N
Now, we can calculate the force of friction:
Force of friction = coefficient of kinetic friction × normal force
We are given that the block accelerates at 0.1 m/s^2, which is the same as saying that the net force on the block is equal to its mass multiplied by acceleration. We can use this information to solve for the force of friction.
Net force = mass × acceleration
(Force of pulling - Force of friction) = mass × acceleration
Given that the mass of the block is 10 kg and the acceleration is 0.1 m/s^2, and the force of pulling is 12 N at a 30 degrees angle, we can calculate the force of friction.
12 N × cos(30 degrees) - Force of friction = 10 kg × 0.1 m/s^2
Simplifying the equation:
6√3 N - Force of friction = 1 N
Force of friction = 6√3 N - 1 N
Force of friction ≈ 9.39 N
Therefore, the force of friction acting on the block is approximately 9.39 N.
D. The coefficient of kinetic friction (uk) can be calculated using the formula:
Coefficient of kinetic friction = Force of friction / Normal force
From the previous calculations, we know that the force of friction is approximately 9.39 N, and the normal force is 98 N. Plugging these values into the formula:
Coefficient of kinetic friction = 9.39 N / 98 N
Coefficient of kinetic friction ≈ 0.0955 or 9.55%
Therefore, the coefficient of kinetic friction (uk) is approximately 0.0955 or 9.55%.
E. To determine the force of static friction required to start the block moving along the floor when a pulling force of 20 N is applied at a 30 degrees angle, we need to find the maximum force of static friction.
The maximum force of static friction can be calculated using the formula:
Maximum force of static friction = coefficient of static friction × normal force
Given that the pulling force is 20 N and acting at a 30 degrees angle, we can calculate the maximum force of static friction:
20 N × cos(30 degrees) = coefficient of static friction × 98 N
Simplifying the equation:
10√3 N = coefficient of static friction × 98 N
Coefficient of static friction = (10√3 N) / (98 N)
Coefficient of static friction ≈ 0.320 or 32%
Therefore, the coefficient of static friction (Us) is approximately 0.320 or 32%.
F. Finally, to find the force of static friction required to start the block moving along the floor, we multiply the coefficient of static friction by the normal force:
Force of static friction = coefficient of static friction × normal force
Using the values from the previous calculations:
Force of static friction = 0.320 × 98 N
Force of static friction ≈ 31.36 N
Therefore, the force of static friction required to start the block moving along the floor is approximately 31.36 N.