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
Show us your work, besides the typing, and someone will assist you. Jiskha is not a do-your-homework-for-you service.
You can certainly do part A
F = ma must be used part B. F consists of two forces.
To solve this problem, we need to break it down into different parts. Let's go step by step:
A. Calculate the weight of the block:
The weight of an object can be calculated using the formula:
Weight = mass × gravitational acceleration
Given that the mass of the block is 10 kg, and the acceleration due to gravity is approximately 9.8 m/s^2:
Weight = 10 kg × 9.8 m/s^2
Weight = 98 N
Therefore, the weight of the block is 98 N.
B. Calculate the force of friction acting on the block:
To calculate the force of friction, we need to use the equation:
Force of friction = coefficient of friction × normal force
Since we don't have the coefficient of kinetic friction (uk) or the normal force (C) yet, we need to solve for those first.
C. Calculate the normal force acting on the block:
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the block is on a horizontal floor, so the normal force will balance the weight of the block.
Normal force = weight of the block = 98 N
Therefore, the normal force acting on the block is 98 N.
D. Calculate the coefficient of kinetic friction (uk):
The coefficient of kinetic friction is a measure of how rough a surface is. It can be determined using the formula:
coefficient of kinetic friction (uk) = force of friction / normal force
Given that the block is accelerating at 0.1 m/s^2, we can use Newton's second law of motion to determine the force of friction:
Force of friction = mass × acceleration
Force of friction = 10 kg × 0.1 m/s^2
Force of friction = 1 N
Plugging the values into the formula, we get:
coefficient of kinetic friction (uk) = 1 N / 98 N
coefficient of kinetic friction (uk) ≈ 0.0102
Therefore, the coefficient of kinetic friction (uk) is approximately 0.0102.
E. Calculate the force of static friction acting on the block:
When the pulling force is 20 N at 30 degrees, the block will start moving along the floor. This implies that the force of static friction between the block and the floor is equal to 20 N.
F. Calculate the coefficient of static friction (us):
The coefficient of static friction is the ratio between the maximum force of static friction and the normal force. In this case, the maximum force of static friction is 20 N, which is equal to the applied force to start moving the block.
Coefficient of static friction (us) = force of static friction / normal force
Coefficient of static friction (us) = 20 N / 98 N
Coefficient of static friction (us) ≈ 0.2041
Therefore, the coefficient of static friction (us) is approximately 0.2041.
To summarize:
A. The weight of the block is 98 N.
B. The force of friction acting on the block is 1 N.
C. The normal force acting on the block is 98 N.
D. The coefficient of kinetic friction (uk) is approximately 0.0102.
E. The force of static friction acting on the block when the pulling force is 20 N at 30 degrees is 20 N.
F. The coefficient of static friction (us) is approximately 0.2041.