Friction

Given:

(m = 2 kg)

=−6[ ]

=−6
v = 2 m/sec

The correct option is (C):

The correct answer is (B) : 0.33

Step 1: Resolve the Force F into Components
The force F can be resolved into horizontal ( ) and vertical ( ) components.

Step 2: Calculate the Normal Force
The normal force (N) acting on the block is given by:

where M is the mass of the block and g is the acceleration due to gravity. Given and , we have:
.

Step 3: Apply the Condition for Impending Motion
The block will just start to move when the horizontal component of the applied force equals the maximum static friction force:

where is the coefficient of static friction. Given , we have:


Multiplying both sides by 8, we get:


.

Conclusion: The block will just start to move when is approximately (Option 4).

1. Maximum Speed on a Curved Road: - The maximum speed of a vehicle on a curved road is given by:

where is the coefficient of friction, g is the acceleration due to gravity, and r is the radius of curvature.

2. Substitute the Values: - , g = 10 m/s², r = 50 m:

Final Answer:

1. Force Equation:

2. Substitute Values: - , , .

3. Solve for :

Step 1: Apply the principle of conservation of momentum.
The total momentum just before and just after the collision is conserved. The initial momentum of the bullet is: The combined mass of the block and bullet after the collision is: Let the velocity of the block and bullet system just after the collision be . From conservation of momentum: Solve for :
Step 2: Use work-energy principle.
The block comes to rest after moving due to the work done against friction. The work-energy principle states: where: The work done by friction is: where is the frictional force and is the distance. Substitute: Solve for :
Final Answer: The coefficient of friction is:

To calculate the work done against friction when a block slides over a surface, we can use the formula for work done against friction, which is given by:

where:

• is the work done against friction (in Joules, J).
• is the force of friction (in Newtons, N).
• is the distance over which the force is applied (in meters, m).

The force of friction can be calculated using the formula:

where:

• is the coefficient of friction.
• is the normal force (in Newtons, N), which is equal to the weight of the block when on a horizontal surface. Hence, , where is the mass (in kg) and is the acceleration due to gravity (approximately ).

Substituting the values into the equation:

Using this value to determine the force of friction:

Now, calculate the work done against friction:

Since the given options and answer rounds the value to 4000 J, the closest correct approximation is:

4000 J

Therefore, the correct answer is 4000 J.

To determine the correct answer, we need to evaluate the accuracy of both statements regarding the nature of friction:

1. Understanding Static Friction:
   • Static friction is the frictional force that prevents two surfaces from sliding past each other.
   • The limiting force of static friction depends on the nature of the surfaces in contact and the normal force, but it is independent of the area of contact.
   • Therefore, Statement I is incorrect because it incorrectly states that the limiting force of static friction depends on the area of contact.
2. Understanding Kinetic Friction:
   • Kinetic friction is the frictional force that acts between surfaces in relative motion.
   • The limiting force of kinetic friction is also independent of the area of contact, but it depends on the materials of the surfaces in contact.
   • Therefore, Statement II is correct, as it correctly states that the limiting force of kinetic friction is independent of the area of contact and depends on materials.

Conclusion: Based on the analysis above, the correct answer is: Statement I is incorrect but Statement II is correct.

Given:
- The angle of inclination, ,
- The acceleration of the block, ,
- The gravitational acceleration, . We need to find the coefficient of kinetic friction, .
Step 1: Analyze the forces acting on the block.
The forces acting on the block include:
- The gravitational force acting vertically downward, which has a component along the incline.
- The normal force, .
- The frictional force opposing the motion, . The net force causing the block to slide down is: The net force is also equal to the mass times the acceleration:
Step 2: Set up the equation.
Equating the two expressions for : Since the acceleration , substitute this into the equation: Canceling out the mass on both sides:
Step 3: Simplify the equation.
Substitute into the equation: Using the known values and : Dividing through by and simplifying: Multiplying through by 2:
Step 4: Solve for .

Final Answer \sqrt{3 - 1}