Question

8) A projectile of mass 0.25 kg moving at 24.0 m/s collides with and sticks to a 1.75-kg block that is connected to a spring for which k = 40.0 N/m, as in the figure below. The block is initially on a frictionless part of a horizontal surface but starts to slide on a rough section immediately after the collision. If the maximum compression of the spring is 0.5 m, what is the force of friction on the block

Answer 1

To find the force of friction on the block, we need to consider the forces acting on it. First, we calculate the normal force, which is the sum of the weight and the force exerted by the spring due to compression. Then, we use the normal force to determine the coefficient of kinetic friction and calculate the force of friction using the equation F_friction = μ * N.

Step-by-step explanation:

To find the force of friction on the block, we need to consider the forces acting on it. The initial velocity of the projectile is given as 24.0 m/s, and its mass is 0.25 kg. The block has a mass of 1.75 kg and is connected to a spring with a force constant of 40.0 N/m. The maximum compression of the spring is given as 0.5 m.

After the collision, the projectile sticks to the block and they start to slide on a rough surface. Since the block starts sliding, the force of friction comes into play. To find the force of friction, we can use the equation:

F_friction = μ * N

where μ is the coefficient of kinetic friction and N is the normal force.

The normal force can be calculated by considering the forces acting on the block in the vertical direction:

1. The weight of the block, which is given by:

• W = m * g
• where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).

The force exerted by the spring due to compression, which is given by:

• F_spring = k * x
• where k is the force constant of the spring and x is the compression of the spring (0.5 m).

Since the block is on a rough surface, there is also a force of friction acting on it. We can determine the coefficient of kinetic friction by considering the forces acting on the block in the horizontal direction:

1. The force exerted by the spring due to compression, which is given by:

• F_spring = k * x
• where k is the force constant of the spring and x is the compression of the spring (0.5 m).

The force of friction, which is given by:

• F_friction = μ * N
• where N is the normal force and μ is the coefficient of kinetic friction that we need to determine.

We can use these equations to find the force of friction on the block.