Question

A 5-meter long ramp is inclined at an angle of 37 degrees above the horizontal. A box that weighs 18 N slides down it. If the coefficient of kinetic friction is uk=0.29, what is the magnitude of the acceleration of the box down the ramp?

a) 2.45 m/s²
b) 3.81 m/s²
c) 4.19 m/s²
d) 5.62 m/s²

Answer 1

To find the magnitude of the acceleration of the box down the ramp, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). The weight of the box can be calculated using the formula weight = mass x gravity (W = mg), where the mass is given as 18 N and gravity is 9.8 m/s². The force of friction can be calculated using the formula frictional force = coefficient of friction x normal force (f = uk x N), where the normal force is the weight of the box multiplied by the cosine of the angle of inclination (N = mg cosθ). The angle of inclination is given as 37 degrees. Once we have the force of friction, we can subtract it from the weight to find the net force acting on the box. Finally, we can use Newton's second law to find the acceleration by dividing the net force by the mass of the box. Using these calculations, the magnitude of the acceleration of the box down the ramp is 3.81 m/s².

Step-by-step explanation:

To find the magnitude of the acceleration of the box down the ramp, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). In this case, the force acting on the box is the force due to gravity (weight) minus the force of friction. The weight of the box can be calculated using the formula weight = mass x gravity (W = mg), where the mass is given as 18 N and gravity is 9.8 m/s².

The force of friction can be calculated using the formula frictional force = coefficient of friction x normal force (f = uk x N), where the normal force is the weight of the box multiplied by the cosine of the angle of inclination (N = mg cosθ). The angle of inclination is given as 37 degrees.

Once we have the force of friction, we can subtract it from the weight to find the net force acting on the box. Finally, we can use Newton's second law to find the acceleration by dividing the net force by the mass of the box.

Using these calculations, the magnitude of the acceleration of the box down the ramp is 3.81 m/s².