To determine the mass of the block, we can use Newton's second law of motion, which states that the force applied to an object is equal to the product of its mass and acceleration:
F = m * a
In this case, the force applied is the horizontal force minus the force of kinetic friction:
F_applied - F_friction = m * a
The applied force is 150 N, and the coefficient of kinetic friction is 0.15. The frictional force can be calculated using the equation:
F_friction = μ * N
Where μ is the coefficient of kinetic friction and N is the normal force. In this case, since the block is on a horizontal surface and not accelerating vertically, the normal force is equal to the weight of the block, which is given by:
N = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting these values into the equation:
150 N - (0.15 * m * g) = m * 2.53 m/s²
To solve for the mass, we rearrange the equation:
150 N = m * (2.53 m/s² + 0.15 * g)
150 N = m * (2.53 m/s² + 0.15 * 9.8 m/s²)
150 N = m * (2.53 m/s² + 1.47 m/s²)
150 N = m * 4 m/s²
Dividing both sides by 4 m/s²:
m = 150 N / 4 m/s²
m ≈ 37.5 kg
Therefore, the mass of the block is approximately 37.5 kilograms.