A 8 kg block is set moving with an initial speed of 6 m/s on a rough horizontal surface. If the friction 12 12 N, approximately how far does the block travel before it stops?
To determine how far the block travels before it stops, we need to use the concept of work and energy. The work done by friction can be calculated using the formula:
Work = Force × Distance
In this case, the force of friction is given as 12 N, and we need to find the distance traveled before the block stops.
The work done by friction is equal to the change in kinetic energy of the block. Initially, the block has kinetic energy due to its initial speed, but when it stops, its kinetic energy becomes zero.
The formula for kinetic energy is:
Kinetic Energy = 0.5 × mass × velocity^2
Given:
Mass (m) = 8 kg
Initial velocity (vi) = 6 m/s
To find the distance traveled by the block, we can use the work-energy principle:
Work by friction = Change in kinetic energy
Substituting the values into the formulas, we have:
12 N × distance = (0.5 × 8 kg × (0 m/s)^2) - (0.5 × 8 kg × (6 m/s)^2)
Simplifying further, we have:
12 N × distance = 0 - (0.5 × 8 kg × (6 m/s)^2)
12 N × distance = -(0.5 × 8 kg × 36 m^2/s^2)
12 N × distance = -(0.5 × 8 kg × 36 m^2/s^2)
12 N × distance = -144 kg × m^2/s^2
Now, we can solve for the distance traveled by the block:
distance = -144 kg × m^2/s^2 / 12 N
distance = -12 kg × m^2/s^2 / N
distance = -(12 kg × m^2/s^2) / N
distance = -12 m^2/s^2
The negative sign suggests that the work done by friction is in the opposite direction of motion. To obtain the magnitude of the distance, we drop the negative sign:
distance = 12 m^2/s^2 / N
≈ 12 m^2/s^2 / 12 N
≈ 1 m
Therefore, the block travels approximately 1 meter before it stops on the rough horizontal surface.