The speed of the blocks when they reach the bottom of the incline depends on the work done by gravity and the work done against friction.

Step 1: Calculate the work done by gravity
The work done by gravity is the same for both blocks because they have the same mass and are dropped from the same height. The work done by gravity is given by W_gravity = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the incline.

Step 2: Calculate the work done against friction
The work done against friction is different for the two blocks because the length of the incline is different. The work done against friction is given by W_friction = μmgcosθd, where μ is the coefficient of friction, m is the mass of the block, g is the acceleration due to gravity, cosθ is the cosine of the angle of the incline, and d is the distance along the incline.

Step 3: Compare the net work done on each block
The net work done on each block is the work done by gravity minus the work done against friction. Because the work done by gravity is the same for both blocks and the work done against friction is greater for the block on the steeper incline (because the distance along the incline is greater), the net work done is greater for the block on the less steep incline.

Step 4: Relate the net work done to the final speed
The net work done on each block is equal to the change in kinetic energy of the block, which is given by ΔKE = 1/2mv^2, where m is the mass of the block and v is the final speed of the block. Because the net work done is greater for the block on the less steep incline, the final speed of this block is greater.

Therefore, Block 1, which is on the less steep incline, is going faster when it reaches the bottom of its respective incline.

Question

The speed of the blocks when they reach the bottom of the incline depends on the work done by gravity and the work done against friction.

Step 1: Calculate the work done by gravity
The work done by gravity is the same for both blocks because they have the same mass and are dropped from the same height. The work done by gravity is given by W_gravity = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the incline.

Step 2: Calculate the work done against friction
The work done against friction is different for the two blocks because the length of the incline is different. The work done against friction is given by W_friction = μmgcosθd, where μ is the coefficient of friction, m is the mass of the block, g is the acceleration due to gravity, cosθ is the cosine of the angle of the incline, and d is the distance along the incline.

Step 3: Compare the net work done on each block
The net work done on each block is the work done by gravity minus the work done against friction. Because the work done by gravity is the same for both blocks and the work done against friction is greater for the block on the steeper incline (because the distance along the incline is greater), the net work done is greater for the block on the less steep incline.

Step 4: Relate the net work done to the final speed
The net work done on each block is equal to the change in kinetic energy of the block, which is given by ΔKE = 1/2mv^2, where m is the mass of the block and v is the final speed of the block. Because the net work done is greater for the block on the less steep incline, the final speed of this block is greater.

Therefore, Block 1, which is on the less steep incline, is going faster when it reaches the bottom of its respective incline.

Knowee AI · Accepted Answer

The speed of the blocks when they reach the bottom of the incline depends on the work done by gravity and the work done against friction.

Step 1: Calculate the work done by gravity
The work done by gravity is the same for both blocks because they have the same mass and are dropped from the same height. The work done by gravity is given by W_gravity = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the incline.

Step 2: Calculate the work done against friction
The work done against friction is different for the two blocks because the length of the incline is different. The work done against friction is given by W_friction = μmgcosθd, where μ is the coefficient of friction, m is the mass of the block, g is the acceleration due to gravity, cosθ is the cosine of the angle of the incline, and d is the distance along the incline.

Step 3: Compare the net work done on each block
The net work done on each block is the work done by gravity minus the work done against friction. Because the work done by gravity is the same for both blocks and the work done against friction is greater for the block on the steeper incline (because the distance along the incline is greater), the net work done is greater for the block on the less steep incline.

Step 4: Relate the net work done to the final speed
The net work done on each block is equal to the change in kinetic energy of the block, which is given by ΔKE = 1/2mv^2, where m is the mass of the block and v is the final speed of the block. Because the net work done is greater for the block on the less steep incline, the final speed of this block is greater.

Therefore, Block 1, which is on the less steep incline, is going faster when it reaches the bottom of its respective incline.

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