If a 60.0 kg person slides down an incline angled 25˚ below the horizontal and friction IS present with a coefficient of kinetic friction equal to k = 0.450. What is the person's acceleration as they slide down the slide.
Wp = m*g = 60kg * 9.8N/kg = 588 N. = Wt. of the person.
Fp = 588*sin25 = 248.5 N. = Force parallel to plane.
Fv = 588*cos25 = 533 N. = Force perpendicular to plane
Fk = 0.450 * 533 = 240 N. = Force of kinetic friction.
Fn = m*a
a = Fn/m = (Fp-Fk)/m
a = (248.5-240)/60 = 0.142 m/s^2.
To find the person's acceleration as they slide down the slide, we can use Newton's second law of motion and consider the forces acting on the person.
First, let's find the force of gravity acting on the person. The force of gravity can be calculated by multiplying the mass of the person (60.0 kg) by the acceleration due to gravity (9.8 m/s^2).
Force of gravity = mass * acceleration due to gravity
= 60.0 kg * 9.8 m/s^2
= 588 N
Next, we need to determine the component of the force of gravity that acts down the incline. This can be found by multiplying the force of gravity by the sine of the angle of the incline.
Force down the incline = Force of gravity * sine(angle)
= 588 N * sin(25˚)
≈ 251.43 N
Since friction is present on the incline, we need to calculate the frictional force. The frictional force can be found by multiplying the coefficient of kinetic friction (k = 0.450) by the normal force. The normal force can be calculated by multiplying the force of gravity by the cosine of the angle of the incline.
Normal force = Force of gravity * cosine(angle)
= 588 N * cos(25˚)
≈ 532.68 N
Frictional force = coefficient of kinetic friction * normal force
= 0.450 * 532.68 N
≈ 239.71 N
Now, let's determine the net force acting on the person down the incline. It is the difference of the force down the incline and the frictional force.
Net force = Force down the incline - Frictional force
= 251.43 N - 239.71 N
≈ 11.72 N
Finally, we can use Newton's second law of motion, F = ma, to find the acceleration of the person. Rearranging the formula, we have:
Acceleration = Net force / mass
= 11.72 N / 60.0 kg
≈ 0.195 m/s²
Therefore, the person's acceleration as they slide down the slide is approximately 0.195 m/s².